Continued Fractions: From Analytic Number Theory to Constructive Approximation
University of Missouri, May 20--23, 1998.
Continued Fractions Conference Continued Fractions: From Analytic Number Theory to Constructive Approximation May 20--23, 1998 Conference Details General Information Abstracts Program Participants Organizing Committee Plenary Speakers Registration Form Travel Information Getting to the Conference by air by car Accomodations On-Campus Dormitories Motels This information is also available for printing in: pdf ps Latex2e
The Lenstra Treurfeest
A conference marking Hendrik Lenstra's retirement from Berkeley. Mathematical Sciences Research Institute and the University of California, Berkeley, CA, USA; 21--23 March 2003.
Lenstra Treurfeest
Integers
On the Occasion of the 65th birthday of Tom Brown. Carrollton, Georgia, USA; 31 October -- 2 November 2003.
Integers Conference 2003 INTEGERS CONFERENCE 2003 On the Occasion of the 65th Birthday of Tom Brown October 31 - November 2, 2003 State University of West Georgia Carrollton, Georgia The Department of Mathematics at the State University of West Georgia is pleased to announce the Integers Conference 2003 in combinatorial number theory. The purpose of the conference is to bring together mathematicians, students, and others interested in combinatorics and number theory. We will also be honoring Professor Tom Brown, on the occasion of his 65 th birthday, for his significant contributions to the field. Schedule Abstracts Travel Location Plenary Speakers: Ronald Graham (UC-San Diego), Euclidean Ramsey Theory Carl Pomerance (Dartmouth), Recent Developments in Primality Testing Melvyn Nathanson (Lehman College, CUNY), Representation Functions of Additive Bases for the Integers Jaroslav Nesetril (Charles University, Prague), Characterization of Ramsey Classes Invited Speakers: Jaclyn Anderson, On the Existence of Rook Equivalent t-core Partitions Miklos Bona, A Simple Proof For the Exponential Upper Bound for Some Tenacious Patterns. Matthew Boylan, Arithmetic Properties of the Partition Function Tom Brown, On the Canonical Version of a Theorem in Ramsey Theory. E. Rodney Canfield, Regularly Spaced Subsums of Integer Partitions Joshua Cooper, Quasirandomness and Continued Fractions Ernie Croot, Critical Sets for Arithmetic Progressions Clay Culver, On Some New Mixed Van Der Waerden Numbers Steve Edwards, Lucas Numbers in the Regular Pentagon Dennis Eichhorn, A Classical Treatment of the Divisibility Properties of Partition Functions Timothy B. Flowers, Difference Density and Aperiodic Sum-Free Sets David Gunderson, Integers and Ramsey Theory Jerrold Griggs, Real Number Channel Assignments with Distance Conditions Neil Hindman, Ramsey-theoretic Consequences of Some New Results About N (and Other Semigroups) Alex Iosevich, Distribution of Lattice Points in Convex Domains: Mean Square Estimates Renling Jin, Inverse Problems for Upper Banach Density Veselin Jungic, About 3-term Arithmetic Rainbow Progressions Omar Kihel, Brocard-Ramanujan Diophantine Equations Zhongshan Li, Reducible Powerful Ray Pattern Matrices Florian Luca, Arithmetic Properties of Motzkin Numbers Rong Luo, On the Degree Sequences of Simple Graphs Karl Mahlburg, Partition Identities and a Theorem of Zagier. Gretchen L. Matthews, Numerical Semigroups Generated by Generalized Arithmetic Sequences Sarah McCurdy, Cutthroat: An All Small Game on Graphs Donald Mills, Avoidability of Sets of Positive Integers Brendan Nagle, Hypergraph Regularity and an Application to Integers Richard Nowakowski, The Game of Clobber Kevin O'Bryant, Fraenkel's Conjecture Paul T. Ottaway, A Parity-Rules Vertex Deletion Game Aaron Robertson, Permutations from Catalan to Fine and Back James Sellers, A Generalization of Overpartitions: Preliminary Results Peter Shiue, On the Partition Function of a Finite Set Pantelimon Stanica, Cholesky Factorizations of Matrices Associated with r-order Recurrent Sequences Todd Will, Generating Maximum Size Shadows David Wolfe, The Structure of the Distributive Lattice of Games Born by Day n Registration: There is no registration fee. Participants are asked to register in advance, if possible, by sending an e-mail message to integers@westga.edu . On-site registration will also be available. Proceedings: Papers presented at the conference will be considered for publication in a special issue of Integers: Electronic Journal of Combinatorial Number Theory. Completed texts must be submitted by February 29th, 2004, and will be handled according to the journal's usual refereeing process. More Information: Please direct your questions to Bruce Landman .
The 4th International Scientific Conference
Modern achievements in number theory and its applications. Tula. September 10-15, 2001.
THE 4th INTERNATIONAL SCIENTIFIC CONFERENCE THE 4th INTERNATIONAL SCIENTIFIC CONFERENCE MODERN PROBLEMS OF THE NUMBER THEORY AND ITS APPLICATIONS TULA TOLSTOY STATE PEDAGOGICAL UNIVERSITY STEKLOV INSTITUTE OF MATHEMATICS MOSCOW LOMONOSOV STATE UNIVERSITY MOSCOW PEDAGOGICAL STATE UNIVERSITY TULA STATE UNIVERSITY CHEBYSHEV SOCIETY Tula, 10-15 September, 2001 Program committee Chubarikov V.N. (chairman), Arkhipov G.I. (vice-chairman), Dobrovolsky N.M. (academic secretary), Preobrazhensky S.N. (execut. secretary), Tureshbaev B.A. (execut. secretary) Program committee-men: Shafarevich I.R., Kuznecov N.V., Lavrik A.F. (Uzbekistan), Lupanov O.B., Matiyasevitch Yu.V., Nesterenko Yu.V., Parshin A.N., Andrianov A.N., Bernik V.I. (Belarus), Bykovsky V.A., Vinogradov A.I., Glukhov M.M., Demidov S.S., Zhuravlyov V.G., Zubkov A.M., Ivanov V.I., Iskovskikh V.A., Karatsuba A.A., Kogan L.A. (Uzbekistan), Konyagin S.V., Korobov N.M., Lavrov I.A., Latyshev V. N., Melnikov I.I., Mitkin D.A., Mikhalyov A. V., Ryshkov S. S., Timofeev N.M., Shidlovsky A.B., Yakovlev A.V., Greaves G. (United Kingdom), Ivic A. (Jugoslavia), Kolesnik G. (USA), Kubilus J. P. (Lithuania), Laurincikas A. (Lithuania), Motohashi Y. (Japan), Narkiewicz W. (Poland), Pan Ch. (China), Ramachandra K.(Indian), Schaal W. (Germany), Schinzel A. (Poland), Tolev D. (Bulgaria), Wolke D. (Germany), Wooley T. D. (USA). OFFICIAL INVITATION MUCH-ESTEEMED COLLEAGUE Regular conference `Modern problems of the number theory and its applications' is dedicated to the anniversaries of the outstanding Russian mathematicians P.L. Chebyshev (180th) and I.M. Vinogradov (110th). The program of the conference involves discussion of modern achievements in number theory and its applications, in the first place made by Russian mathematicians, and preparation and discussion of materials for publishing of monograph under the primary title `Number theory in XX century'. The work of the sections on the following directions is planned: analytic, algebraic and elementary number theory, Diophantine analysis and transcendental numbers, geometry of numbers, the teaching of number theory, the history of its development, algebra, discrete mathematics, number theoretic methods and proximate analysis. We invite you to take part in the work of the conference. We will be waiting for your claim designed according to the following standard form till 1, March, and the thesis of your report till 15, May. Our electronic addresses are chubarik@mech.math.msu.su and dobrovol@tspu.tula.ru (send it to both addresses). The thesis should not occupy more than 1 page in LaTeX-2.09 with the following preamble: \documentstyle[14pt]{article} \textwidth=160mm \textheight=260mm \pagestyle{empty} \begin{document} \begin{center} {\large \bf TITLE}\\ {\bf authors (in parentheses: city)}\\ {\bf e-mail} \end{center} Thesis received by the Organizational Committee will be published at the expense of payments of the participants of the conference ($20). Please visit the Internet server of Tula Tolstoy State Pedagogical University www.tula.net tgpu or e-mail dobrovol@tspu.tula.ru for additional information including bank accounts. Organizational Committee. CLAIM Name Phone, e-mail Academic degree, rank Subject of report Place of work, duty Section (direction) Post address
Paul Erds and his Mathematics
Hungarian Academy of Sciences, July 4-11, 1999.
Paul Erdos and His Mathematics Paul Erds and his Mathematics Budapest, July 4-11, 1999 The Hungarian Academy of Sciences , The Jnos Bolyai Mathematical Society , TheEtvs Lornd University of Budapest and The Mathematical Institute of The Hungarian Academy of Sciences , organized a conference dedicated to the memory of Paul Erds that was held July 4 - 11, 1999, in Budapest , Hungary . The topics of the conference included all basic fields that Paul Erds contributed to: Analysis (including Ergodic Theory), Combinatorics (including Combinatorial Algebra, Combinatorial Geometry and Theoretical Computer Science), Number Theory, Probability Theory, and SetTheory among others. The main goal of the conference was to explore Paul Erds' wide ranging contributions to mathematics, to bring us closer to an understanding of his rich oeuvre, and to attempt to survey the trends of development originating in his work. This symposium was a satellite conference to the UNESCO-ICSU World Conference on Science held 26 June - 1 July 1999, in Budapest, Hungary. List of participants text xls pdf If your e-mail or other data has changed please let us know so we could update the list! The Proceedings of the Conference have now been published by the Bolyai Society and Springer. Detailed information (list of contents, how to order from Springer, price etc.) can be found at Springer's webpage . The table of contents can also be found here: Volume 1 Volume 2 The Conference Site Detailed program Dvi PostScript Full booklet of the Program Dvi PostScript (including alphabetical list of speakers) A musical tribute to Paul Erds written by Peter Winkler
14th Czech and Slovak International Conference on Number Theory
Covers elementary, analytical and algebraic number theory. Tatra mountains, Slovakia, September 6-10, 1999.
14th Czech and Slovak International Conference on Number Theory
Midwest Algebraic Number Theory Day
University of Illinois at Chicago, USA; 10 May 2003.
Midwest Algebraic Number Theory Day
PIMS Number Theory Group Thematic Summer Program
Diophantine Number Theory and Mahler's Measure of Polynomials. Simon Fraser University. June 2-29, 2003.
PDEfest Pacific Institute for the Mathematical Sciences PIMS Number Theory Group Thematic Summer Program June 2-29, 2003 Simon Fraser University Mahler's Measure of Polynomials We would like to announce the special month of our thematic summer program (2003) on Diophantine Number Theory at Simon Fraser University (SFU) , sponsored by Simon Fraser University and the Pacific Institute for the Mathematical Sciences (PIMS) . These thematic summer programs are coordinated by the PIMS Number Theory Group , which consists of number theorists from University of British Columbia , University of Calgary , University of Washington and Simon Fraser University . The theme of this summer program is on the Mahler's measure of polynomials and the program will be held at SFU in the period of June 2-29, 2003 . Professor Jeffrey D. Vaaler from the University of Texas at Austin will be our PIMS Distinguished Visitor this year and he will deliver a lecture series in the second and third weeks of June, 2003. A graduate course will be taught by Stephen Choi (SFU) in the first week to serve as a preliminary to the Distinguished Lectures. Finally, a small and focused workshop will be held after the lecture series in the third or fourth weeks. This summer program is designed to be small and focused. This summer program is also designed to coordinate with the BIRS workshop on " The many aspects of Mahler's measure " April 26 - May 01, 2003 . Arrival and Accommodation Information Schedule of the program Schedule of Distinguished Lecturer Series by Jeff Vaaler Notes of Jeffrey Vaalers Lectures: [1] [2] [3] [4] Notes of Mike Mossinghoffs Lectures: [1] Notes of Stephen Chois Lectures: [1] [2] [3] [4] Notes of Corentin Pontreaus Lectures: [1] Confirmed Participants Iskander Aliev ( Technische Universitat Wien ) Arthur Baragar (UNLV) Jason Bell ( University of Michigan ) M.J. Bertin (Institut de Mathematiques, Equipe de Theorie des Nombres) David Boyd ( University of British Columbia ) Edward Dobrowolski (The College of New Caledonia ) Tamas Erdelyi ( Texas , AM) Kevin Hare ( University of California , Berkeley ) Angel Kumchev ( University of Texas , Austin ) Friedrich Littmann (UIUC, UBC, SFU) Michael Mossinghoff ( Davidson College ) Nathan Ng ( Universit de Montral) Chris Pinner ( Kansas State University ) Igor E. Pritsker ( Oklahoma State University ) Georges Rhin (Universit de Metz) Christopher Rowe ( University of Colorado , Boulder , UBC, SFU) Jeff Vaaler ( University of Texas , Austin ) Alf van der Poorten (Centre for Number Theory Research, Macquarie University ) Carlo Viola (Universit di Pisa) M. Qiang Wu (Universite de Metz) Ping Zhou ( St. Francis Xavier University ) (Graduate Students) Shabnam Akhtari (SFU) Adrian Belshaw (SFU) John Condon ( University of Texas , Austin ) Jeremy Coffelt ( Kansas State University ) Amanda Folsom ( UCLA ) Lenny Fukshansky ( University of Texas , Austin ) Mostafa Ibrahim (October 6 University, Cairo ) Samy Khemira (Universit de Paris) Joshua Knauer ( Dalhousie University ) Matilde Lalin ( University of Texas , Austin ) Pei Li (SFU) Christine Liu (UC, Berkeley) Alan Meichsner (SFU) Idris Mercer (SFU) Sonny Monhammadzadeh (UC, Davis) Keshav Mukunda (SFU) Clay Petsche ( University of Texas , Austin ) Corentin Pontreau (Universit de Caen) Mathew Rogers ( University of British Columbia ) Joe Rusinko ( Univeristy of Georgia ) Kyle Schalm ( University of Texas , Austin ) Chris Sinclair ( University of Texas , Austin ) Juan Carlos Trujillo (UC, Berkeley) Maryam Verdian-Rizi (SFU) Soroosh Yazdani ( University of Michigan ) If you are interested in participating in our summer program, please let us know. Organization committee Stephen Choi (Chair) ( kkchoi@cecm.sfu.ca ) Peter Borwein ( pborwein@cecm.sfu.ca ) Imin Chen ( ichen@sfu.ca ) Ron Ferguson ( rferguson@pims.math.ca ) 2003 Pacific Institute for the Mathematical Sciences Last Modified: Tuesday, 17-Jun-2003 15:09:58 PDT
Journes Arithmtiques XXIII
Karl-Franzens Universitt Graz, Graz, Austria. July 6-12, 2003.
XXIIIrd Journes Arithmtiques Graz 2003 XXIIIrd Journes Arithmtiques Graz 2003 July 6th - July 12th 2003
International Conference on Arithmetic Geometry
Research Training Network Arithmetic Algebraic Geometry. Regensburg, Germany. May 6-10, 2002.
Midterm review of the RTN network "Arithmetic Algebraic Geometry" Research Training Network Arithmetic Algebraic Geometry International Conference on Arithmetic Geometry (May 6-10, 2002) Midterm Review (May 11, 2002) Regensburg The conference will be held under the auspices of the European Research Training Network Arithmetic Algebraic Geometry with support from the University of Regensburg. The principal nodes of the Network are the Universities of Barcelona, Bonn, Cambridge, Durham, Jerusalem, Mnster, Orsay, Padova, Paris 13, Regensburg, Rennes, and Strasbourg. The aim of the conference is to cover broadly important recent developments in arithmetic geometry. Topics include the advances in p-adic Hodge theory, p-adic differential equations, automorphic forms, Iwasawa theory, and the Birch-Swinnerton-Dyer conjecture. In keeping with the aims of this Network, the conference will include not only the plenary talks of the senior invited speakers, but young researchers in the field will be asked to present their recent work as well. The Conference will take place at the University of Regensburg . Scientific Committee: Massimo Bertolini (Padova) Jean-Marc Fontaine (Paris-Sud) Guy Henniart (Paris-Sud) Uwe Jannsen (Regensburg) Norbert Schappacher (Darmstadt) Anthony J. Scholl (Cambridge) Invited Speakers: L. Berger (Brandeis) V. Berkovich (Weizmann-Institut) C. Bertolin (Strasbourg) J.-B. Bost (Paris-Sud) M. Cailotto (Padova) L. Fargues (Paris 7) C. Greither (UniBw Mnchen) R. Litcanu (Rennes 1) S. Marcello (Regensburg) Z. Mebkhout (Paris 7) D. Petrequin (Cambridge) G. Racinet (Mnster) M. Spie (Nottingham) M. Strauch (Mnster) T. Tsuji (Tokyo) E. Urban (Paris 13) O. Venjakob (Heidelberg) A. Yafaev (Imperial College London) D. Zagier (MPI Bonn Collge de France) Travel Information Hotel Information Registration Form Conference Information Schedule of the meeting (subject to last minute changes) List of participants Conference poster postscript (Din A4), jpg (Din A4), Microsoft-Word (Din A3) Last Change; 07.05.2002 Lars Brnjes
L-functions and Automorphic forms
Supported by the National Science Foundation and the Clay Mathematics Institute. Johns Hopkins University, Baltimore. May 14-17, 2002.
L-Functions and Auotmorphic Forms L-Functions and Automorphic Forms Conference Johns Hopkins University, Department of Mathematics The Johns Hopkins University is sponsoring a Conference on L-Functions and Automorphic Forms in mid-May 2002, supported by the National Science Foundation, the Clay Mathematics Institute, and the JHU Department of Mathematics. May 14-17, 2002 Lectures to be held in Krieger 205 Registration be held in Krieger 209 Organizers: Arthur Jaffe, CMI Dinakar Ramakrishnan, Caltech Freydoon Shahidi, Purdue Steven Zelditch, Johns Hopkins In Honor of Joe Shalika's 60th Birthday Invited Participants (Many of Whom Will Be Speakers): William Casselman (UBC) James Cogdell (Oklahoma State U) Sol Friedberg (Boston College) Steve Gelbart (Weizman Institute, Rehovot) Masaaki Furusawa (Osaka, Japan) Thomas Hales (U Pittsburgh) Herve Jacquet (Columbia U) Dihua Jiang (Univ of Minnesota) Nicholas Katz (Princeton) Henry Kim (U Toronto) Stephen Kudla (U of Maryland) Philip Kutzko (U of Iowa) V.Lakshmibai (Northeastern U) Erez Lapid (Ohio State U) Ilya Piatetski-Shapiro (Yale) Dinakar Ramakrishnan (Caltech) Stephen Rallis (Ohio State U) Paul Sally (U of Chicago) Peter Sarnak (Princeton, NYU) Freydoon Shahidi (Purdue) Ramin Takloo-Bighash (Princeton) Yuri Tschinkel (U Penn)
JAMI 2003
Japan-U.S. Mathematics Institute conference on primes and knots. March 7-16, 2003, Johns Hopkins University
JAMI Home Japan-U.S. Mathematics Institute (JAMI) and Johns Hopkins University, Department of Mathematicsis sponsoring a conference on Primes and Knots March 7 - 16, 2003 Primes and Knots Organizers:Stavros Garoufalidis, Toshitake Kohno, Jack Morava, Masanori Morishita, Steven Zucker List of Speakers: Dror Bar-Natan, Nigel Boston, Katia Consani, Charles Frohman, Kazuhiro Fujiwara, Hidekazu Furusho, Stavros Garoufalidis, William Goldman, Kazuo Habiro, Joanna Kania-Bartoszynska, Mikhail Kapranov, Atsushi Katsuda,Louis Kauffman, Akio Kawauchi, Toshitake Kohno, Sadayosi Kojima, Shin-Ya Koyama, Masato Kurihara, Thang Le, Barry Mazur, Masanori Morishita, Hitoshi Murakami, Kunio Murasugi, Ken'ichi Ohshika, Makoto Sakuma, Yuji Shimizu, Adam Sikora, Yuichiro Taguchi, Tomohide Terasoma, Dylan Thurston, Hiroshi Tsunogai, Masakazu Yamagishi, Yoshiyuki Yokota.
Arithmetic Geometr Algorithmic Number Theory Program, MSRI
Algorithmic Number Theory Program, MSRI, 11-15 December 2000, Berkeley.
SITE MAP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SEARCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SHORTCUT: Choose a Destination... Calendar Programs Workshops Summer Grad Workshops Seminars Events Announcements Residence Program Math Circles BAMO Application Materials Visa Information Propose a Program Propose a Workshop Policy on Diversity MSRI Alumni Archimedes Society Why Give to MSRI Ways to Give to MSRI Donate to MSRI Planned Gifts FAQ Mission Governance Staff Member Directory Contact Us Directions For Visitors Pictures Library Computing SGP Video Lectures MSRI in the Media Emissary Newsletter Outlook Newsletter Subscribe to Newsletters Books, Preprints, etc. Federal Support Corporate Affiliates Sponsoring Publishers Foundation Support Academic Sponsors HOME ACTIVITIES AT MSRI PROPOSALS APPLICATIONS ALUMNI DEVELOPMENT ABOUT MSRI COMMUNICATIONS SUPPORT SPONSORS Calendar Programs Workshops Summer Graduate Workshops Seminars Events Announcements Past Projects Math Circles BAMO Arithmetic Geometry December 11, 2000 to December 15, 2000 Organized By: Noam Elkies, William McCallum, Jean-Franois Mestre, Bjorn Poonen (chair) and Ren Schoof Parent Programs: Algorithmic Number Theory The workshop will focus on the development of explicit and computational methods in arithmetic geometry, as well as the complexity analysis of existing algorithms. Topics include (but are not necessarily limited to) computational aspects of the following: determination of rational points on curves and higher dimensional varieties Mordell-Weil groups of elliptic curves and other abelian varieties Selmer and Shafarevich-Tate groups isogenies, endomorphism rings, and torsion subgroups of abelian varieties minimal proper regular models of curves Neron models and conductors of Jacobians equations for modular curves and Shimura curves function field analogues of all the above zeta functions of curves and other varieties over finite fields. For more information: Questions about this workshop should be sent either by email to msri-workshops@msri.org or by regular mail to: Arithmetic Geometry Mathematical Sciences Research Institute 17 Gauss Way, Berkeley, CA 94720-5070. USA The Institute is committed to the principles of Equal Opportunity and Affirmative Action. Back to Workshop Listing Want to be kept updated on upcoming events? Then Click Here to Subscribe to Our Newsletters! HOME | ACTIVITIES AT MSRI | PROPOSALS APPLICATIONS | ALUMNI DEVELOPMENT | ABOUT MSRI | COMMUNICATIONS | SPONSORS AFFILIATES Copyright 2005 All Rights Reserved. Mathematical Sciences Research Institute. Privacy Policy Legal Information Contact Us
International Conference dedicated to D.K. Faddeev
EIMI, St. Petersburg, June 30-July 5, 1997.
International Algebraic Conference dedicated to D.K.FADDEEV June 24 - 30, 1997 Announcement The St.Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences The St.Petersburg State University The conference is timed to the 90th anniversary of Dmitrii Konstantinovich Faddeev (1907-1989), an eminent scientist and a wonderful man. He was an Associate Member of Academy of Sciences of the Soviet Union, Professor in the St.Petersburg State University, a State prize laureate, President of the St.Petersburg Mathematical Society. D.K.Faddeev contributed significantly to many areas of mathematics. It is expected that many outstanding specialists in algebra and its applications will participate in the conference. The pupils of Faddeev, the pupils of his pupuls, and so on consider the participation in the conference their pleasant duty. It is anticipated that plenary reports will be given and the work of the following sections will be organized: algebraic geometry, algebraic number theory, Galois theory, representation theory, rings and modules, the theory of groups and semigroups, algorithmic and numerical problems of algebra. One session is planned to be dedicated to Vera Nikolaevna Faddeeva (1906-1983). We ask all who wish to participate the conference to respond by June 30 and inform the coordination comittee about their suggestions. The coordination committee needs to know at least an approximate list of participants in order to plan further actions. Chairman of Coordination Committee Doctor of Physics and Mathematics, Professor A.V.Yakovlev Secretary of Coordination Committee Candidate of Physics and Mathematics, Assistant Professor B.B.Lur'e Mail address: Russia, 191011, St.Petersburg, Fontanka 27, POMI Russia, 198904, St.Petersburg, Staryi Petergof, Bibliotechnaya square, 2. Department of Algebra and Number Theory. Fax: 7(812)-310-53-77 E-mail address: Lurje@pdmi.ras.ru EIMI home page
China-Japan Seminar: Refinements of number-theoretic methods
March 12-15, 2001, Graduate School of Advanced Technology, University of Kinki.
China-Japan Seminar : Refinements of number-theoretic methods China-Japan Seminar Refinements of number-theoretic methods March 12-16 2001 at Graduate School of Advanced Technology University of Kinki Iizuka, Fukuoka, Japan sponsored by the JSPS (Japan Society for the Promotion of Science) and organized by S. Kanemitsu, Univ. of Kinki, Iizuka and Chaohua Jia, Academia Sinica All interested are cordially welcome. Mar. 12 (Mon.) 13:25-13:30 Opening address and acknowledgements 13:30-14:10 Prof. Yoshinobu Nakai (Yamanashi Univ.) A candidate for cubic theta-Weyl sums 14:10-14:20 Break 14:20-15:00 Prof. Pan Chengbiao (The China Agricultural Univ.) Developements of analytic number theory in China 15:00-15:20 Break 15:20-16:00 Prof. K. Nagasaka (Hosei Univ.) Developements of analytic number theory in Japan (for general audience) 16:00-16:10 Break 16:10-16:50 Prof. Shigeki Egami (Toyama Univ.) Values at positive integers of the Dedekind zeta-function of a totally real field 16:50-17:00 Break 17:00-17:40 Prof. Leo Murata (Meijigakuin Univ.) On a distribution property of the residual order of a (mod p) (joint work with Mr. Chinen) Mar. 13 (Tue.) 9:30 -10:20 Prof. Christopher Deninger (Univ. Munster ) Number theory and dynamical systems on foliated spaces 10:20-10:40 Break 10:40-11:30 Prof. Brunello Tirozzi (Univ. of Rome) Neural networks and its applications 11:30-11:40 Break 11:40-12:20 Prof. Junjiro Noguchi (Univ. of Tokyo) Some results in view of Nevanlinna theory 12:20-14:00 Lunch Break 14:00-14:40 Prof. L. Weng (Nagoya Univ.) New local and global non-Abelian zeta functions for elliptic curves 14:40-15:10 Break 15:10-15:50 Prof. Yoshio Tanigawa (Nagoya Univ.) and Dr. M. Yoshimoto (RIMS) Ramanujan's formulas and automorphic forms 15:50-16:10 Break 16:10-16:50 Prof. Zhang Wenpeng (North-West Univ.) On a problem of D.H.Lehmer and general Kloosterman sums 16:50-17:00 Break Parallel Session 17:00-17:40 Prof. Masanori Katsurada (Keio Univ.) On an asymptotic formula of Ramanujan for a certain theta-type series 17:00-17:40 Prof. S. Kanemitsu (Univ. of Kinki) The susmna principle in number theory (for general audience) 18:00- Reception Party at Nogami President Hotel Mar. 14 (Wed.) (Free) Morning: Free discussion Afternoon: Excursion to Mt. Aso Mar. 15 (Thu.) (Misc. Day) 9:30 -10:20 Prof. Winfried Kohnen (Univ. Heidelberg) Special values of L-series of automorphic forms at the central point 10:20-10:40 Break 10:40-11:20 Prof. Shigeki Akiyama (Niigata Univ.) Purely periodic orbits of arithmetic algorithms 11:20-11:40 Break 11:40-12:20 Prof. T. Matala-Aho (Univ. of Oulu) Iterated q-functional equations and irrationality measures 12:20-14:00 Lunch Break 14:00-14:40 Dr. M. Nagata On G functions and approximation (RIMS) 14:40-15:00 Break 15:00-15:40 Prof. Masaaki Amou (Gunma Univ.) Arithmetical properties of certain q-functions 15:40-16:00 Break 16:00-16:40 Prof. Tianxin Cai (Hang Zhou Univ.) Congruencials, binomial coefficients and Fermat's last theorem 16:40-17:00 Break Parallel Session 17:00-17:40 Prof. Ryotaro Okazaki (Doshisha Univ.) On class number problem and least prime residue 17:00-17:40 Prof. K. Alladi (Univ. of Florida) The Indian mathematical genius Ramanujan - a peek into his magical world of identities (for general audience) Mar. 16 (Fri.) 9:30-10:20 Prof. K. Miyake (Tokyo Metropolitan Univ. ) Some aspects on interactions between algebraic number theory and analytic number theory 10:20-10:40 Break 10:40-11:30 Prof. K. Alladi (Univ. of Florida) Going beyond the (big)theorem of Gollnitz - a breakthrough in the theory of partitions and q-series 11:30-11:40 Break 11:40-12:00 Dr. T. Horie (Suzuka Inst. of Techn.)and Mr. S. Kanou (Nagoya Univ.) A generalization of the Dedekind eta function 12:00-14:00 Lunch Break 14:00-14:40 Prof. K. Matsumoto (Nagoya Univ.) Zeta-functions defined by two polynomials (A joint work with L.Weng) 14:40-15:10 Break 15:10-15:50 Prof. Chaohua Jia (Academia Sinica) On the distribution of alpha p modulo one 15:50-16:00 Break 16:00-16:40 Prof. Minggao Lu (Shanghai Univ.) Some applications of sieve method {wpU w(Z~i[) Z~i[_I@W PRNRPQ()PU() EwBHw sX {\@@Eww@YZp \@`I zA W[@w@w RPQ () 13:25-13:30 A 13:30-14:10 M (Rw) RV[^|Ca 14:10-14:20 xe 14:20-15:00 `F rI p (_wEkw) _W 15:00-15:20 xe 15:20-16:00 (@w) {_W(u) 16:00-16:10 xe 16:10-16:50 ] (xRw) ffLg[[^_l 16:50-17:00 xe 17:00-17:40 c (w@w) a (mod p)]z (mOGi) RPR () 9:30-10:20 NXgt@[EfjK[ (~X^[w) tw_wn 10:20-10:40 xe 10:40-11:30 ulEeBb`([}w) j[lbg[Np 11:30-11:40 xe 11:40-12:20 Y(w) l@i_ 12:20-14:00 H 14:00-14:40 EF(w) ~CVICA[x[[^ 14:40-15:10 xe 15:10-15:50 JDj (w)Eg (sw) }kW^` 15:50-16:10 xe 16:10-16:50 EF y W (kwEw) D.H.[}[N[X^[}a 16:50-17:00 xe su 17:00-17:40 jcI (cw) e[^^}kWQ 17:00-17:40 (Ew) _XVi[ (u) 18:00- vWfgzeZvV p[eB[ RPS () (R) CRCChR RPT () 9:30 -10:20 Bt[gER[l (nCfxNw) ^`LS_l 10:20-10:40 xe 10:40-11:20 HR (Vw) _IASYIO 11:20-11:40 xe 11:40-12:20 ^pj }^-GCz(E[[w) q-x 12:20-14:00 Hxe 14:00-14:40 ic(sw) G 14:40-15:00 xe 15:00-15:40 VH (Qnw) q-_I 15:40-16:00 xe 16:00-16:40 eBG V c@C(YBw) CQWCtF}[I 16:40-17:00 xe su 17:00-17:40 Y (uw) CM]f 17:00-17:40 NViX~ AfB(t_w) ChYVw}kW- q- (u) RPU () 9:30 -10:20 O (sw) I__pl@ 10:20-10:40 xe 10:40-11:30 NViX~ AfB(t_w) Qjbc()-q-_VWJ 11:30-11:40 xe 11:40-12:00 x]Y(ut)E[j(ww@) ffLg G[^ 12:00-14:00 Hxe 14:00-14:40 {k (w) Q`[[^ ( EF) 14:40-15:10 xe 15:10-15:50 `I zA W[ (w@w) alpha pW[1z 15:50-16:00 xe 16:00-16:40 ~ KI [ (Cw) @p
15th Annual Automorphic Forms workshop
24-29 March 2001, American Institute of Mathematics (AIM), Palo Alto, CA
THE 15TH ANNUAL WORKSHOP ON AUTOMORPHIC FORMS AND RELATED TOPICS List of Participants Preliminary schedule of talks WHERE: American Institute of Mathematics (AIM), Palo Alto, CA ARRIVAL DATE: Saturday, 24 March 2001 DEPARTURE DATE: Thursday, 29 March 2001 ORGANIZER: Brian Conrey (conrey@aimath.org) DESCRIPTION: Over the last 14 years, the Annual Workshop has remained a small and friendly conference. Those attending range from new PhD's to well established researchers. For young researchers, the conference has provided support and encouragement; for accomplished researchers, it has provided the opportunity to mentor as well as a forum for exchanging ideas. The atmosphere is always friendly, never confrontational. Topics include, among others, classical theory of automorphic forms, Siegel modular forms and integral quadratic forms. GENERAL INFORMATION: As usual, there is a $25 registration fee. This money will be used to buy snacks, like fresh bagels, fruit, fresh juice, coffee and tea (and halfhalf) at breakfast time, as well as lighter snacks, coffee and tea throughout the day. In addition, your registration fee pays for your own conference coffee mug (out of which you must drink the available liquids), and for the conference party. Each participant is strongly encouraged to give a talk (typically, 20, 40 or 60 minutes in length -- your choice). In March, the weather in Palo Alto is usually pretty good, but you can expect some rain. TRANSPORTATION: Palo Alto is located equidistant from San Jose International Airport (SJC) and San Francisco International Airport (SFO). AIM is about 4 blocks away from the California Ave stop on Cal Train. Both airports have free shuttles to and from Cal Train Stations (more details) . ACCOMODATIONS: You need to make your own hotel reservation. I recommend Hotel California, but they have a very limited number of spots. (List of hotels near to AIM with approximate prices.) FUNDING: There may be some funding available. If you would like to apply for funding, please send me the following information by 10 January, 2001: Your name, institution, position, airfare. WHAT YOU SHOULD DO NOW: If you think you will be attending this workshop, you should send e-mail to Brian Conrey, at conrey@aimath.org to say that you expect to attend. You are encouraged to say whether you will be speaking, and if so, for how long.
Workshop on L-functions and Random Matrices
May 14-18, 2001, American Institute of Mathematics, Palo Alto, California.
WORKSHOP ON L-FUNCTIONS AND RANDOM MATRICES WHERE: American Institute of Mathematics (AIM), Palo Alto, CA DATES: Monday, May 14 - Friday, May 18, 2001 ORGANIZER: Brian Conrey (conrey@aimath.org) List of Participants Some open problems Schedule of talks Hotels where everyone is staying DESCRIPTION: In 1974, H. Montgomery found the first indication of a connection between the distribution of the zeros of the Riemann zeta-function and the distribution of the eigenvalues of random matrices. Random matrices had been studied by statisticians beginning in the 1930s and Mathematical Physicists starting in the 1950s. In 1981, numerical calculations by A. Odlyzko of some statistics of the zeros of the Riemann zeta-function led to remarkable graphs illustrating the connection that Montgomery predicted. Recent work by many authors, has led to several interesting developments including the study of low lying zeros of families of L-functions and conjectures for mean-values of L-functions running in a family. The purpose of this workshop is to consider the future development of this field, with a focus on understanding the goals of the subject, the limitations, and how to attack the important unsolved problems. PARTICIPATION: There is a limited amount of space for participants for this workshop. If you would like to attend and can make a case that your participation would be of benefit to your research program, please contact Brian Conrey (conrey@aimath.org).
Winter Meeting of the Canadian Mathematical Society
London, Ontario, Canada. December 7-9, 1996.
Number Theory Schedule: Number Theory Session Organizer: R. Murty (Queen's), e-mail: murty@mast.QueensU.CA Saturday, December 7 10:10-10:40am: Henri Darmon (McGill) 10:45-11:15am: Kumar Murty (Toronto) 11:15-11:45am: Damien Roy (Ottawa), "Algebraic approximation and algebraic independence" Abstract: dvi , postscript 2:40-3:10pm: John Friedlander (Toronto), "Prime values of a thin polynomial sequence". Abstract: dvi , postscript 3:15-3:45pm: Alberto Perelli (Genoa), "The exceptional set of primes in short intervals". Abstract: dvi , postscript 3:45-4:15pm: David Dummit (Vermont), "Computations related to Rubin's version of Stark's Conjecture". Abstract: dvi , postscript 4:15-4:45pm: Chris Cummins (Concordia), "Modular equations and the genus zero property of moonshine functions". 4:45-5:15pm: Jan Minac (Western), "Galois 2-extensions". Abstract: dvi , postscript Sunday, December 8 9:00-10:00am: Plenary speaker: Dinakar Ramakrishnan (Caltech), "Determination of modular forms and motives by twists of critical L-values". Abstract: dvi , postscript 10:10-10:40am: Chantal David (Concordia), "Average Frobenius Distributions of Elliptic Curves". Abstract: dvi , postscript 10:45-11:15am: Cam Stewart (Waterloo), "Towards the abc conjecture". Abstract: dvi , postscript 11:15-11:45am: Ernst Kani (Queen's), "A Problem of Mazur". 2:40-3:10pm: H. Kisilevsky (Concordia) 3:15-3:45pm: Georg W. Nowak (Vienna), "Fractional part sums and lattice points". Abstract: dvi , postscript
Galois theory and modular forms conference
Organized by Ki-ichiro Hashimoto and Hiroaki Nakamura Tokyo Metropolitan University. September 25-29, 2001.
Galois theory and modular forms -- Program "Galois Theory and Modular Forms" September 25 --- 29, 2001 Tokyo Metropolitan University International House Organizers: Ki-ichiro Hashimoto (Waseda U.), Hiroaki Nakamura (TMU.) * Supported by Grant-in-Aid for Scientific Research [(B)(1) 11440013, Katsuya Miyake] September 25 (Tue) 10:30-11:30 Ken Ono (Univ. of Wisconsin, Madison): "Coefficients of half-integral weight modular forms" 11:45-12:45 Masanobu Kaneko (Kyushu Univ.): "On certain modular forms arising from a differential equation of hypergeometric type" 3:00-4:00 Michael Dettweiler (Univ. of Heidelberg) "On some l-adic representations coming from geometry" 4:15-5:15 Yuichi Rikuna (Waseda Univ.): "Explicit constructions of generic polynomials for some elementary groups" September 26 (Wed) 10:30-11:30 Scott Ahlgren (Univ. of Illinois at Urbana-Champaign): "Modular forms and congruences for the partition function" 11:45-12:45 Hidenori Katsurada (Muroran Institute of Tecnology) "Special values of the standard zeta functions of modular forms" 3:00-4:00 Hyunsuk Moon (Kyushu Univ.): "On the nonexistence of certain Galois extensions" 4:15-5:15 Masafumi Imaoka, Yasuhiro Kishi (Tokyo Metropolitan Univ.): "A certain relation between dihedral extensions and Frobenius extensions" September 27 (Thu) 10:30-11:30 B.Heinrich Matzat (Univ. of Heidelberg): "The Differential Abhyankar Conjecture" 11:45-12:45 Yoshiyuki Kitaoka (Meijo Univ.): "On the distribution of units in Galois extensions over Q" [Afternoon session is free] September 28 (Fri) 10:30-11:30 Masato Kuwata (Kanagawa Institute of Technology) : "Mordell-Weil group of an elliptic curve and Galois extensions" 11:45-12:45 Armand Brumer (Fordham Univ.): "Existence and non-existence results for curves of low genus" 3:00-4:00 Takehito Shiina (Tohoku Univ.): "Regular Galois Realizations of PSL_2(p^2) over Q(T)" 4:15-5:15 Ki-ichiro Hashimoto (Waseda Univ.): "On Noether's problem for A_n (tentative)" [5:30-- Party] September 29 (Sat) 10:30-11:30 Hiroshi Ito (Kanagawa Univ.): "Some results concerning cubic Gauss sums and elliptic functions" 11:45-12:45 Hiroaki Nakamura (Tokyo Metropolitan Univ.): "Dedekind sums, free differential calculus and anabelian geometry" 3:00-4:00 Masanori Morishita (Kanazawa Univ.): "Analogies between knots and primes, 3-manifolds and number fields" 4:15-5:15 Shinichi Mochizuki (RIMS, Kyoto Univ.): "On the anabelian geometry of p-adic local fields" (URL) http: www.comp.metro-u.ac.jp ~h-naka Galois01 galois01.html Back to Homepage (Access information etc.)
Multilinear Algebra and Additive Number Theory
The workshop will be held at Complexo Interdisciplinar da Universidade de Lisboa. March 24-26, 2002. Lisbon, Portugal.
mult-alg Workshop Multilinear Algebra and Matroid Theory March 24-26, 2002 Lisbon, Portugal The workshop will be held at Complexo Interdisciplinar da Universidade de Lisboa. A plan of the area is available in GIF format. Schedule Invited speakers Olga Azenhas (Univ. de Coimbra, Portugal) Abstract pdf dvi Ravindra Bapat (Indian Statistical Institute, India) Abstract pdf dvi Rajendra Bhatia (Indian Statistical Institute, India) Abstract pdf dvi Antnia Duffner (Univ. de Lisboa, Portugal) Abstract pdf dvi Rosrio Fernandes (Univ. Nova de Lisboa, Portugal) Abstract pdf dvi Robert Guralnick ( Univ. Southern Calif., Los Angeles, USA) Abstract pdf dvi Leonid Gurvits (Los Alamos National Laboratory, USA) Abstract pdf dvi Joseph Kung ( Univ. North Texas, Denton, USA) Abstract pdf dvi Chi-Kwong Li (The College of William and Mary, USA) Abstract pdf dvi Russell Merris (Cal. State Univ., Hayward, USA) Guedes de Oliveira (Univ. do Porto, Portugal) Abstract pdf dvi Thomas Pate (Auburn University, USA) Title "Extreme Rays for Cones of Generalized Matrix Functions" Ilda da Silva (Univ. de Lisboa, Portugal) Abstract pdf dvi Bruce Sagan (Michigan State Univ., USA) Abstract pdf dvi George Soules (Institute for Defense Analysis, La Jolla, USA) Abstract pdf dvi Neil White (University of Florida, Gainsville, USA) Abstract pdf dvi Minisimposium There will be a minisimposium on "Multilinear Algebra and Additive Number Theory" organized by Melvyn Nathanson (Abstract pdf dvi ) CUNY, USA. Minisimposium Speakers Cristina Caldeira (Univ. Coimbra, Portugal) Abstract pdf dvi Jean-Marc Deshouillers (Univ. Bordeaux, France) Abstract pdf dvi Shalom Eliahou (Univ. Calais, France) Abstract pdf dvi Gregory Freiman (Tel Aviv Univ., Israel) Abstract pdf dvi Luis Gallardo (Univ. Brest, France) Abstract pdf dvi Georges Grekos (Univ. St. Etienne, France) Abstract pdf dvi Alain Plagne (Ecole Polytechnique, Paris, France) Abstract pdf dvi Qing Xiang (University of Delaware, USA) Abstract pdf dvi In addition to the lectures by the invited speakers it is planned a limited number of Contributed talks . Contributed Talks Alexandre Borovik (UMIST, UK) Abstract pdf dvi Henrique Cruz (Univ. da Beira Interior, Portugal) Abstract pdf dvi Bernd Fiedler (Univ. Leipzig, Germany) Abstract pdf dvi Ricardo Mamede (Univ. de Coimbra, Portugal) Abstract pdf dvi Leiba Rodman (The College of William and Mary, USA) Abstract pdf dvi Rita Simes (Univ. de Aveiro, Portugal) Abstract pdf dvi Information Fernanda Proena Av. Prof. Gama Pinto 2 1649-003 Lisboa, PORTUGAL email: mult-alg@hermite.cii.fc.ul.pt site: hermite.cii.fc.ul.pt ~mult-alg Accommodation The participants are asked to contact the following travel agency, directly. ARTE VIAGENS- Viagens e Turismo Lda Tel: 351-212733917 Fax: 351-212733867 email: arteviagens@ip.pt HOTELS Reserves should be made as soon as posssible Organizers Richard Brualdi J.A. Dias da Silva Amlia Fonseca Carlos Gamas Hans Schneider William Watkins Support Centro de Estruturas Lineares e Combinatrias Centro de Matemtica da Universidade de Coimbra Faculdade de Cincias da Universidade de Lisboa International Linear Algebra Society Fundao Para a Cincia e a Tecnologia Support of "Programa Operacional Cincia, Tecnologia, Inovao do Quadro Comunitrio de Apoio III"
Birch-Swinnerton-Dyer Conjecture
Special semester Princeton University, NJ, USA; Fall 2003.
Special Semester on the Birch-Swinnerton-Dyer Conjecture Special semester on the Birch-Swinnerton-Dyer Conjecture Princeton University, Fall 2003 In Fall 2003, Princeton will host a special semester devoted to the Birch-Swinnerton-Dyer conjecture. Henri Darmon, Ravi Ramakrishna, and Chris Skinner are visiting the department; Darmon and Skinner will give semester-long seminars (see descriptions below) and Andrew Wiles will give a graduate course. From 5-8 November there will be an AIM workshop at Princeton detailing recent progress on topics related to B-S-D, organized by Andrew Wiles, Henri Darmon, Jordan Ellenberg, and Chris Skinner. Tentative schedule of lectures: 5 Nov 10:30 Andrew Wiles: Introduction 11:30 Shin-ichi Kobayashi: "Iwasawa theory for elliptic curves at supersingular primes." 2:30 Robert Pollack: "The main conjecture for CM elliptic curves at supersingular primes." 4:00 Henri Darmon: "Stark-Heegner points and Kronecker's solution to Pell's equation." 6 Nov 10:00 Chris Skinner: "L-values for GL(2) and an Eisenstein ideal for GU(2,2)." 11:30 Eric Urban: "On the main conjecture for ordinary elliptic curves." 2:30 Vinayak Vatsal: "Special values of Rankin L-functions." 4:00 Shou-Wu Zhang: "On the Gross-Zagier formula." 7 Nov 10:00 Douglas Ulmer: "What is known over function fields." 11:30 Susan Howson: "Non-abelian Iwasawa theory with applications to the arithmetic of elliptic curves." 2:30 Keith Conrad: "Partial Euler products on the critical line." 4:00 Emmanuel Kowalski: "Variation of the rank and related invariants in families of elliptic curves." 8 Nov 10:00 Noam Elkies: "Heegner point constructions for curves x^3 + y^3 = k." 11:30 William Stein: "Connections between the visibility of Shafarevich-Tate groups and the Birch-Swinnerton-Dyer conjecture." All talks will take place at Taplin Auditorium in Fine Hall (Princeton Math Department.) The conference will begin on the morning of 5 Nov and conclude with lunch on 8 Nov. Other confirmed participants include A.Agashe, M. Bertolini, P. Green, M. Harris, B. Howard, A.Iovita, M. Kurihara, A.Logan, L. Merel, K. Rubin, D. Savitt, O. Venjakob, T. Weston. The most convenient airport to Princeton is Newark (EWR). More detailed information about traveling to Princeton can be found here . Many visitors are staying at the Holiday Inn, from which a free shuttle will take you to the conference each morning and to which it will return you in the evening; if you're interested in staying there, please e-mail Scott Kenney at skenney@math.princeton.edu to assure yourself of the conference rate. Funding may be offered, subject to availability. Skinner's Seminar: L-values and orders of Selmer groups Weds, 3-4:30 pm, Fine 1201 starting 1 Oct In this seminar, I will explain an approach to proving the Main Conjecture of Iwasawa Theory for elliptic curves and for elliptic modular forms in general. This conjecture relates the p-adic properties of the values L(E,\chi,1), E an elliptic curve with multiplicative or ordinary reduction at p and \chi a character of p-power conductor, to those of the p-part of certain Selmer groups (Galois cohomology groups) attached to E. This approach makes use of the arithmetic of Eisenstein series and p-adic modular forms for the unitary group U(2,2) and of Galois representations associated to cuspforms for this group. The results obtained through this approach, when combined with work of Kato and assuming some expected properties of the Galois representations, prove many instances of the Main Conjecture. I will assume familiarity with the theory of elliptic modular forms and some acquaintance with automorphic forms on higher rank unitary groups* (such as Hermitian modular forms) from both the classical and adelic points of view. *As discussed in Shimura's book "Euler products and Eisenstein series," for example. Darmon's seminar: Rational Points on Modular Elliptic Curves Thursday, 1-2:30 pm, Fine 801 Starting 25 Sep The goal of this seminar is to discuss the notion of Heegner points on modular elliptic curves as well as certain conjectural variants, and the information they provide on the Birch and Swinnerton-Dyer conjecture. Topics to be covered (roughly in chronological order) will include: 1. Classical Heegner points attached to imaginary quadratic fields. 2. Proof of Kolyvagin's theorem and its application to the Birch and Swinnerton-Dyer conjecture. 3. The rudiments of rigid analysis and p-adic uniformisation. 4. The notion of "Stark-Heegner" points introduced in [1]. 5. Relation with p-adic L-functions attached to Hida families. 6. A proof of some cases of the main conjecture of [1] (work in progress with M. Bertolini). References: [1] H. Darmon. Integration on ${\cal H}_p\times{\cal H}$ and arithmetic applications. Annals of Mathematics 154 (2001) 589-639. [2] H. Darmon. Rational points on modular elliptic curves. NSF-CBMS Lectures, August 8-12 2001, to appear. Can be downloaded from: http: www.math.mcgill.ca darmon pub pub.html (Note: It is better to download the .ps version if you want some figures to print correctly.) last revised 22 Sep 2003
West Coast Number Theory Conference 2003
Asilomar Conference Center, Monterey (Pacific Grove) CA, USA; 17--21 December 2003.
West Coast Number Theory Conference 2003 December 17 (Evening Banquet) through December 21st (Lunch) Asilomar Conference Center in Monterey (Pacific Grove), California 1. Contact Information 2. How to Register 3. Directions to Asilomar 4. Financial Support (WE'RE FUNDED!!!) 5. Problem Sets 6. Program from 2001 7. Format of the Conference 8. Service and Thanks 9. Asilomar's Webpage 1. Contact Information: Organizer: Bart Goddard 2508 Spruceleaf Circle Austin, TX 78757 goddardb@newsguy.com Personal Note: I've terminated my relationship with Concordia University at Austin, so I'm using my personal contact information to organize this conference. I am reluctant to put my home phone on this site, however, and I'm sorry if that creates an inconvenience for anyone. My number is NOT unlisted, and conferees are welcome to brave both the trials of Directory Assistance and the low probability that my offspring won't be tying up the line if they feel a telephone conversation is necessary. Voicemail exists. 2. How to register: A. Hurry! We do seem to be competing (somewhat fiercely) with other groups at Asilomar for space. Rooms are on a first come basis and seem to be going fast. My guess is that you need to get your reservation in by Sept. 15th to be comfortable. But I'm also sure that later dates will still get you a room on grounds. Many people stay off grounds in local motels. It would help me if those people would also hurry and register too, since Asilomar is hounding me for accurate head counts already. B. If you are planning on staying on grounds, print this Word document , fill it out and send it with your payment directly to Asilomar (note that this includes four nights and all meals). Note that vegetarian meals and other dietary options are available. C. Download and print this Word document and send it with your registration fee to me. Please note that this means that you need to write two checks and send them to two different places. Asilomar takes credit cards, but I do not. A couple of notes: In the past, we've had enough spouses staying on grounds and few enough conferees staying off grounds that things have balanced out. But the last two times at Asilomar, there have been uncomfortable situations in which the number of chairs I've needed in the meeting room has exceeded the number of beds rented, which raises the management's eyebrows. As I explained at the business meeting two years ago, off-grounds attendees (number theorists, but not spouses, etc.) will have to start paying the daily use fee, which is $8 per day, no matter how short the day is. So for a person attending all of the conference and staying off grounds, I've added a $40 charge to my registration form. If you will not be there for the entire 5 days then feel free to make your own adjustment to this fee, by pro-rating for the number of days you'll be present. (Attending the banquet counts as a day.) The upside to the daily use fee is that it buys off grounds people the right to eat in the Asilomar dining hall. (Non-number theorists would have to pay the fee in order to eat at the dining hall.) Having paid the fee, prices for meals are: (Adult) Breakfast: $7.16, Lunch $9.72, Dinner $15.54 (Child 3-12 years old) Breakfast: $6.05, Lunch $6.94, Dinner $12.22, all including tax. A non-number theorist staying off grounds needs to pay the fee only on days that he eats in the dining hall. Because we're trying to save the "historic" rooms for those on a budget, we're not allowing those rooms to be rented for single occupancy. So if you want the luxury of a single room, then you have to also indulge yourself the luxury of a "standard" room. (We're really thinking of saving the historic rooms for graduate students, but it's first come, first served.) 3. How to get there. By Air: Monterey has an airport serviced by major airlines. Taxis, rental cars and public transportation are available from there to the Asilomar Conference Grounds. Driving directions and maps are avialable on Asilomar's website: Directions Peter Montgomery, our resident expert on California's train system, has provided these directions for getting to Asilomar without driving: Those coming from San Francisco and San Jose airports can take the Monterey-Salinas Airbus to Monterey Transit Plaza in downtown Monterey for $30. Reservations are recommended. Greyhound also serves Monterey Transit Plaza (N.B. this is separate from the Monterey Greyhound station). Amtrak has connecting buses to Salinas and San Jose Amtrak stations. Monterey-Salinas Transit (MST) route A connects Monterey Transit Plaza to the Asilomar entrance (and to Monterey Aquarium) for $1.75. MST route 21 serves Monterey airport but does not run on Sunday. 4. Support: To apply for funding, download this Word document, which is two pages and I hope self-explanatory, and follow the directions therein. Hard copies of this document will be available at the conference. If you can get it together and turn all the stuff in to me at the conference, that's A-OK. But I think most folk won't be able to until sometime in January. I'm setting the deadline for applying for funds at January 31st. The sooner we all get our stuff in, the sooner we can disburse the funds. BUT, if someone needs more time, it's easy to push the deadline back, because, heck, it's just me, and I can change it if I want to. So just let me know if you need a few extra days (e.g., your letter writer is out of town or something.) A. WE ARE FUNDED!!! For U.S Citizens, the NSA will support travel, room and board, and registration expenses for conference attendance for graduate students, the unemployed, and junior faculty who do not otherwise have full support. (Two years ago, I was able to spend only half of the grant, which is bad. So I need to stress that junior faculty should not be shy about asking for funds, lest we be in danger of having the amount of support cut. I'm happy to listen to sentences like "OK, I'll apply for support, but if you run out of money, then I should be the one to not get any" and use my own judgement for distribution of funds. So please ask for money.) The amount of the award is $9,850. Usually everyone gets whatever they ask for. In the years we run short, the method of distribution has been to fund everyone at a constant percentage (as far as I know always 90%.) (p.s. I'm going to try to get an advance against the grant this time, in order to avoid the massive delays we had two years ago, which was caused mostly by the NSA and Office of Naval Research having never heard of Concordia. Now they know. Hopefully no graduate students will be eating maccheese until August waiting for checks this time. I think end of March at the latest.) B. The Number Theory Foundation has agreed again to complement the NSA's support by supporting the travel for non-US citizen graduate students who otherwise do not have support. There is usually a cap on the amount of support per person. The amount of the award is $1500. The details about how to divide this money are worked out after the requests come in. The committee and the organizer meet and try to meet the needs in a fair and reasonable way. C. The application procedure for BOTH grants is identical. Just keep all your receipts. There will be a form available at the conference, and downloadable from this site, which will be filled out and mailed to me after you get back home and have your final expenses tallied. Also, we will need a short letter of support from a supervisor (advisor or department head or dean, say) saying that 1. attendance at this conference is a good idea, 2. that there is not other support available OR that the available support is partial and what the extent of that partial support is, and 3. the letter MUST verify the citizenship status of the applicant so that we can pay out of the correct fund. So that's three things: Receipts + form + letter. D. As always, if something's not clear, shoot me an e-mail. 5. The Problems: Here is the Problem Set from the 2002 Conference at San Franciso: PDF Version of Problem Set Problems from the 2001 conference at Asilomar: PostScript Version of Cover Page PostScript Version of Problem Set PDF Version of Cover Page PDF Version of Problem Set DVI Version of Cover Page DVI Version of Problem Set Problems from the 2000 conference in San Diego: PostScript Version of Cover Page PostScript Version of Problem Set DVI Version of Cover Page DVI Version of Problem Set PDF Version of Cover Page PDF Version of Problem Set 6. Program from 2001 Conference Here is the Word document listing the speakers and their titles from the 2001 West Coast Number Theory Conference which was held at Asilomar. I make it available to give an idea of the participant list and the wide variety and level of talks one can expect at this conference. (This document may not reflect last minute changes that were made to the program.) 2001 Schedule of Talks 7. Format of the Conference: We will begin with an opening banquet on the evening of Dec. 17 at 6 pm. Attendence at the banquet is optional, and there is an additional surcharge of $8 for the meal (which means that the cost for off-grounds attendees is $23.) After dinner, we will retire to the meeting room, which is currently assigned as Heather (see the map in the directions link), where we'll have a quick meeting where titles are submitted and a schedule of talks is hastily assembled. People who skip the banquet are welcome to meet the rest of us at Heather. Tentatively we'll schedule this meeting for 7:30 pm. (The surcharges for the special entrees for banquets are quite pricy. I'm most likely to choose "Chicken Asilomar" yet again, because it's half the price of the others. I think the idea is more the commeraderie than paying $16 +$8 daily use fee +$15 dinner fee = $39 for a plate of Asilomar's version of smoked salmon. So chicken will be the "meat entree", and there will be a vegetarian option, which is currently listed as "Vegetarian Wellington" involving white beans and fontina cheese. People wanting Kosher or Vegan or other options should contact Asilomar directly.) The length allowed for all talks is usually about 15 minutes, including time for questions. Dec. 18 and 20 will be full days of talks, while Dec. 19 will have talks in the morning, leaving the afternoon for our "afternoon off" for sightseeing and recreation. Dec. 21 will be another half day. Two problem sessions will be scheduled during the conference, where unsolved problems are presented (and Peter Montgomery will proceed to solve them ;-)) The results from previous problem sessions are given below. The second problem session will most likely be on the morning of Dec. 21. An overhead projector is provided for talks. The chalkboards that have been available in the past have been woefully inadequate. If you need anything like computer projection equipment or computers, then it's strictly BYO. I do bring a small supply of blank transparencies and markers, but they get snarfed up quickly by non-self-sufficient attendees. I'll try to get you whatever you need if I have enough lead time, but I recommend that you bring your own stuff, and not rely on my limited resourcefulness. 8. Service and Thanks: I am happy to help in any way. If downloading the forms doesn't work, then I can e-mail or snail mail them. If you know of someone who wants to be added to the e-mail or snail mail list, then please let me know or have them mail me. Corrections and additions to this page are welcome. (And I know they are forthcoming ;-)) Thanks to David Cantor who maintains the wntc.org domain, Lawrence Szu who maintains our mirror site, Gerry Myerson who maintains the problems sets, The Number Theory Foundation, and others who do things that keep things running smoothly.
p-adic Variation of Motives
Banff, Alberta, Canada; 13--18 December 2003.
p-adic variation of motives with the participation of p-adic variation of motives December 13 - 18, 2003 Organizers: Kevin Buzzard (Imperial College), Robert Coleman (UC Berkeley), Matthew Emerton (Northwestern Univ.), Eyal Goren (Univ. McGill) Objectives The workshop will bring together researchers currently investigating the p-adic variation of motives. The goal of the workshop is two-fold: to report on recent progress, and to focus attention on the many open problems that remain in the field. Recent progress. There has been significant progress in the study of p-adic variation of motives in the last year or so, and one goal of the workshop is to report on this progress. Relations with p-adic Hodge theory. The p-adic Galois representations attached to classical motives are potentially semi-stable in the sense of Fontaine, and so it is quite reasonable to hope for relations between Fontaine's theory and the theory of p-adic variation of motives. Recently concrete progress has been made in establishing this connection.Iovita has associated a Fontaine-Dieudonn\'ee module to a Hida family and shown that it has rank one over the parameter space. More generally, Kisin has made an extensive analysis of the p-adic Hodge theory of the family of Galois representations attached to Coleman's finite-slope families. As a consequence, he has verified the Fontaine-Mazur conjecture for such Galois representations: if the Galois representation occurring in such a family is potentially semi-stable at p then it arises from a classical modular form. Slopes of modular forms. Buzzard has extensive computational evidence suggesting some remarkable patterns in the variations of slopes of classical modular forms. Together with Frank Calegari he has proven them in a special case. More precisely, they have shown that if m\ge 0 and if n is sufficiently large then for any k 0 such that 2^n|k, the first few 2-adic slopes of weight k forms on \Gamma_0(2) are equal to 1+2\,\ord_2((3n)! n!), each slope occurring with multiplicity one. Gouvea has also performed extensive computations of slopes, and likewise has discovered suprising and so-far unexplained phenomena. p-adic deformations of automorphic forms. One approach to constructing a family of p-motives containing a given classical motive is to first construct a p-adic analytic deformation of a corresponding automorphic form, and then to construct an accompanying deformation of the p-adic Galois representation attached to the given motive. Indeed, this was the approach used by Hida in order to deform the motives attached to ordinary modular forms, and by Coleman and Mazur in order to deform the motives attached to finite-slope modular forms. Recently, Kassaei has developed a theory of overconvergent p-adic automorphic forms attached to certain quaternion algebras, which allows him to construct p-adic analytic families of finite slope eigenforms for these quaternion algebras. As with Coleman's construction of families of modular eigenforms of finite slope, his approach depends on exploiting the p-adic geometry of the appropriate Shimura curve, using techniques of rigid analysis. Ash and Stevens have developed another approach to interpolating finite slope automorphic forms on GL_n, using cohomological methods. More precisely, they are able to find p-adic analytic families of group cohomology classes that are finite-slope eigenclasses for an appropriate Hecke operator at p. Emerton has initiated yet another approach to the problem of p-adically interpolating automorphic forms, which uses methods from the emerging theory of locally p-adic analytic representations of p-adic reductive groups. Applying his results to the representations constructed out of the cohomology of congruence subgroups, he is again able to construct p-adic analytic families of finite slope eigenclasses. When the reductive group in question gives rise to a Shimura variety, the functorial nature of his approach allows him to also construct corresponding families of Galois representations. p-adic variation over finite fields. Wan has recently established Dwork's conjecture on the meromorphicity of the fixed slope parts of the L-function attached to families of varieties defined over a finite field. Overconvergence and p-adic limiting techniques play a key role in the proof. Open problems. There are many fundamental open questions related to the p-adic variation of motives, and a second goal of the workshop is to focus the attention of experts on these problems, and develop some lines of attack. Some of the most pressing open questions are: Can one establish the existence of the universal family (or any non-trivial family) of p-motives containing a given classical motive? What is the geometric nature of this universal family? How are the classical motives situated in this universal family? Can one intrinsically characterize those p-adic Galois representations which are p-motives belonging to such a deformation space (for example, in terms of their p-adic Hodge theory)? How should one formulate the ``main conjecture of Iwasawa theory'' for a general family of p-motives? In the case of the eigencurve, the computations of Buzzard provide a hint as to the answer to the second of these questions, and the results of Kisin go a long way to suggesting an answer to the fourth. The representation-theoretic methods of Emerton provides a new point of view on the first and third. It seems likely that before we can fully understand the form that a ``main conjecture'' should take, it will be crucial to understand more closely the relationship between the variation of p-motives and p-adic Hodge theory. By bringing together those people who are investigating these and related questions, and sharing our knowledge of the most current developments and techniques available in the field, the workshop should lead to a significant improvement in our understanding of all three of these questions, and the many other important open questions in the field. Mathematical implications of the workshop. Each improvement in our understanding of the p-adic variation of motives has led to concrete developments in number theory and arithmetic geometry. For example, Hida's theory provided a crucial tool in Greenberg and Stevens' proof of the elliptic curve case of the Mazur-Tate-Teitelbaum conjecture on the L-invariant. As mentioned above, it also led to Mazur's theory of deformations of Galois representations. This theory in turn was fundamental to Taylor and Wiles' proof of Fermat's last theorem, as well as to recent progress of Buzzard, Dickinson, Shepherd-Barron and Taylor on the Artin conjecture. More recently, Coleman's construction of one parameter families of non-ordinary finite-slope eigenforms has been used by Stevens to prove the general case of Mazur-Tate-Teitelbaum conjecture, and (as mentioned as above) by Kisin to establish cases of the Fontaine-Mazur conjecture. In light of this history, we expect that further developments in the theory of p-adic variation will have similarly far-reaching consequences for number theory as a whole. The proposed workshop would play a pivotal role in stimulating such developments. Confirmed Participants Programme Videos Click image for larger photo. 2005 Banff International Research Station
Arithmetic Geometry and Number Theory
Conference to honour Nicholas M. Katz on his 60th birthday. Princeton, NJ, USA; 11--14 December 2003.
Arithmetic Geometry and Number Theory - Main Page Main Page Conference Schedule Conference Participants Arithmetic Geometry and Number Theory Conference to Honor Nicholas M. Katz on his 60th birthday. December 11 - 14, 2003 Princeton University Mathematics Department Speakers Include: Jean-Benoit Bost Aise Johan deJong Pierre Deligne Helene Esnault Gerd Faltings Benedict H. Gross Christopher Hooley Mark Kisin Neal Koblitz Barry Mazur Philippe Michel John Tate Organizing Committee: Brian Conrey Gerard Laumon Peter Sarnak Andrew Wiles Funding Sources: National Science Foundation American Institute of Mathematics Princeton University Mathematics Department1 For more information about the conference please e-mail dona@princeton.edu
Quadratic Forms, Algebraic Groups, and Galois Cohomology
Banff International Research Station, Alberta, Canada; 4--9 October 2003.
Quadratic forms, algebraic groups, and Galois cohomology with the participation of Quadratic forms, algebraic groups, and Galois cohomology October 04 - 09, 2003 Organizers: R.Elman (UCLA), A.S.Merkurjev (UCLA), J.Minac (Univ. Western Ontario), C.Riehm (McMaster Univ.) Objectives The principal objective of the workshop is the dissemination of recent results and techniques in the subject areas of the meeting. Perhaps the most important of these centers around Voevodsky's work. His resolution of the Milnor conjecture has already given rise to further important developments by many people, most of whom will be attending the workshop. The meeting will be run in the Oberwolfach tradition - speakers will be selected at the meeting itself, ample time will be left for discussions, and there will be an afternoon hike during the conference. Confirmed Participants Videos Final Report (in PDF format) Click image for larger photo. 2005 Banff International Research Station
Number Theory, Arithmetic Geometry and Algebra
In honour of Georges Gras. University of Besanon, France; 16--18 October 2003.
Conference Number Theory, Arithmetic Geometry and Algebra in honor of Georges GRAS october 15 -- 18, 2003 At the occasion of the departure to the retirement of Georges GRAS, the Department of Mathematics of Besanon organizes a conference intitled "Number Theory, Arithmetic Geometry and Algebra" on october 15 -- october 18, 2003. To accede to the Department, see the french version Talk schedule A volume of Journal de Thorie des Nombres de Bordeaux will be dedicated to Georges Gras. Confirmed speakers include: B. Angls (Universit de Caen) E. Bayer (Ecole Polytechnique de Lausanne) D. Benois (Universit de Bordeaux) H. Cohen (Universit de Bordeaux) J. Cougnard (Universit de Caen) J. Cresson (Universit de Besanon) G. Frei (Universit Laval, Qubec) D. Hayes (University of Massachusetts, Amherst) D. Hoffmann (Universit de Besanon) F. Hajir (University of Massachusetts, Amherst) J.-F. Jaulent (Universit de Bordeaux) H. Lenstra (Universit de Leiden) H. Lombardi (Universit de Besanon) S. Louboutin (Institut de Math. de Luminy) J. Martinet (Universit de Bordeaux) A. Mzard (Universit Paris XI) C. Movahhedi (Universit de Limoges) T. Nguyen Quang Do (Universit de Besanon) H. Oukhaba (Universit de Besanon) B. Perrin-Riou (Universit Paris XI) R. Schoof (Universit Rome 2) C. Soul (IHES) M. Waldschmidt (Universit Paris VI) This conference is funded by: University of Besanon , Department of Mathematics of Besanon , European Network GTEM (Besanon, Bordeaux, Leiden, Rome), GDR of Number Theory, and the Algo team of GRIMM Toulouse 2 . For any other information, please contact: Christian Maire , Jean-Robert Belliard or Hassan Oukhaba .
Voronoi Conference 2003
Third Vorono Conference on Analytic Number Theory and Spatial Tessellations. Institute of Mathematics, Kyiv (Kiev), Ukraine; 22--28 September 2003.
Voronoi Conference-2003 First Circular Ukrainian version VORONO CONFERENCE On Analytic Number Theory and Spatial Tessellations 1. General Information 1.1 Introduction The Institute of Mathematics of the National Academy of Sciences of Ukraine (NASU), the T.Shevchenko Kyiv National University, the M.Gogol Nizhyn State Pedagogical University, the Ukrainian International Committee for Science and Culture of the NASU, and the Ukrainian Mathematical Society would like to announce the Third Vorono Conference on Analytic Number Theory and Spatial Tessellations to be held in Kyiv from September 22 to 28, 2003. September 22 is the arrival day. The Conference will be organized in honour of the eminent Ukrainian Mathematician Georgy Vorono (1868-1908) who was born in Zhuravka, a small village some 160km east of Kyiv. The Conference will take place in Kyiv at the Institute of Mathematics of the NASU and at the National University. The organizing committee will make all efforts you could enjoy your stay in Kyiv. 1.2 Organizing Committee Anatolij Samoilenko (Ukraine), Chairman, Peter Engel (Switzerland), Vice-Chairman, Halyna Syta (Ukraine), Secretary; Tatiana Karataeva, Vasyl Ostrovskyi, Natalia Ryabova, Anatolij Serdyuk, Halyna Shvets, Yaroslav Vynnyshyn, Irina Yegorchenko - Institute of Mathematics of the NASU; Mykola Perestyuk, Mykola Nazarenko, Andrij Yurachkivs'kyi - Kyiv Shevchenko National University; Vasyl Yakovets - Nizhyn Pedagogical University. Conference Address: Vorono Conference Dr. H.Syta Inst. of Mathematics Nat. Acad. Sci. Ukraine Tereshchenkivska Str.,3 01601, Kyiv-4, Ukraine E-mails: syta@imath.kiev.ua or karat@imath.kiev.ua 1.3 Program Committee The Conference will include the following sections: Number Theory; Vorono Method of Summation of Divergent Series and Integrals; Probability Models for Vorono Tessellations; Lattice Packings; Applications of Vorono Diagrams. The members of the Program Committee responsible for the corresponding sections include: Antanas Laurin\v{c}ikas (Lithuania), Andrzej Schinzel (Poland), Anatolij Kochubei (Ukraine); Liliya Boitsun (Ukraine), Myroslav Gorbachuk (Ukraine); Chiu Sung Nok (Hong-Kong), Igor Kovalenko (Ukraine); Peter Engel (Switzerland), Robert Erdahl (Canada), Sergei Ryshkov (Russia), Volodymyr Sharko (Ukraine); Christopher Gold (Canada), Masaharu Tanemura (Japan), Yaroslav Yatskiv (Ukraine). 1.4 Travel and Accommodation Participants should make their own travel arrangements to Kyiv. A Conference bus will transfer participants from the Airport or Railway Station to the Institute of Mathematics of the NASU. All participants will be accommodated in nearby hotels of different categories of their choice. 2. Scientific Program The scientific program consists of full and short lectures. Abstracts should be submitted in English until May 15, 2003. Abstracts will be distributed at the beginning of the Conference. The lectures will be presented at the auditories both of the Institute of Mathematics and of the University. Full lectures of 45 minutes will be given in the morning session. Short lectures of 20-30 minutes will be held in parallel sessions in the afternoon. Overhead projection facilities will be available. 3. Social Events In the evening of the arrival day, Monday, September 22, an informal come-together meeting will take place. In the afternoon of Thursday, September 25, the conference excursion to the historical monuments of golden Kyiv will be organized. The conference banquet will take place in the evening of Friday, September 26. For accompanying persons sightseeing tours to Kyiv and its surroundings will be organized each day at a low price. 4. After-Conference Excursion From September 27 to 28, conference participants have the possibility to take part in a two days' after-conference excursion to Zhuravka, the native-place of Georgy Vorono and his burial-place, and to ancient Chernigiv and Nizhyn, staying the night in the City Hotel in Nizhyn. If you would like to receive further information, please, mail us to the conference address, and please indicate the sections of your interest.
Analytic Number Theory and Surrounding Areas
Research Institute of Mathematical Science, Kyoto, Japan; 29 September -- 3 October 2003.
Analytic Number Theory and Surrounding Areas Analytic Number Theory and Surrounding Areas Date: 29 Sep. - 3 Oct. Place: RIMS (Research Institute of Mathematical Science) Kyoto, JAPAN Organizer: Shigeki AKIYAMA (Niigata Univ.) PROGRAM ( Japanese Version , DVI file , PDF file ) Monday 29 Sep. 10:00 - 10:50 Michio Ozeki (Yamagata Univ.) Mass formula for the Jacobi weight enumerators of type II codes and some relationships of it with Jacobi forms 11:00 - 11:50 Winfried Kohnen (Univ. Heidelberg Germany) Estimating Fourier coefficients of Siegel modular forms 13:30 - 14:00 Takao Komatsu (Hirosaki Univ.) From continued fractions to real numbers 14:00 - 14:30 Yukio Ohkubo (Inter. Univ. Kagoshima) On the discrepancy of the sequences (na+f (n)) 14:30 - 15:00 Rie Natsui (Keio Univ.) Principal convergents and mediant convergents associated to a-continued fractions 15:30 - 16:00 Yumiko Ichihara (Waseda Univ. JSPS) The convergence of L-functions associated with Hilbert cusp form 16:00 - 16:30 Takaaki Tanaka (Keio Univ.) Algebraic independence of certain power series associated with d-adic expansion of real numbers Tuesday 30 Sep. 9:00 - 9:50 Masanobu Kaneko (Kyushu Univ.) On modular forms satisfying a certain differential equation 10:00 - 10:50 Edward Burger (Williams College USA) On a question of Davenport and a quantitative refinement of the Markoff Spectrum 11:00 - 11:40 Shigeru Kanemitsu (Kinki Univ.), Yoshio Tanigawa (Nagoya Univ. ), Haruo Tsukada (Kinki Univ.), Masami Yoshimoto (Nagoya Univ. JSPS) An application of zeta functions 13:30 - 14:20 Noriko Hirata-Kohno (Nihon Univ.) Linear forms in p-adic logarithms and abc conjecture 14:30 - 15:00 Hidehiko Mishou (Nagoya Univ.), Hirofumi Nagoshi (Niigata Univ. JSPS) On value distribution of quadratic L-functions 15:30 - 16:00 Yuichi Kamiya (Nagoya Univ. JSPS) On spectrums of certain harmonic functions attached to the Riemann zeta-function 16:00 - 16:30 Takeshi Kurosawa (NTT SI Lab.) Arithmetic properties of reciprocal sums of binary recurrences 16:45 - 17:15 Chiharu Kaminishi (Keio Univ.) Estimates of automorphic L-functions in the d-aspect 17:15 - 18:00 Jun'ichi Tamura A new approach to higher dimensional continued fractions Wednesday 1 Oct. 9:00 - 9:50 Okazaki Ryotaro (Doshisha Univ) Counting integer points by Baker theory and basic math 10:00 - 10:50 Attila Peth (Debrecen Univ. Hungary) Generalized radix representations and dynamical systems 11:00 - 11:50 Yoichi Motohashi (Nihon Univ. ) A Vista of Mean Zeta Values, Part 2 Afternoon Free Time Thursday 2 Oct. 9:00 - 9:50 Stphane Louboutin (Univ. Caen France) Effective bounds for Zeta and L-functions, with applications to the Brauer-Siegel theorem 10:00 - 10:50 Gilles Lachaud (CNRS France) Eisenstein series and the Riemann Hypothesis 11:00 - 11:30 Shin'ichiro Okada (Keio Univ.), Iekata Shiokawa (Keio Univ.) q,r number system and algebraic independence 13:30 - 14:20 Shunji Ito (Kanazawa Univ.) Purely periodic beta expansions with Pisot basis 14:30 - 15:00 Leo Murata (Meijigakuin Univ.), Koji Chinen (Osaka Inst. Tech.) On a distribution property of the residual order of a ( mod p), IV 15:30 - 16:00 Yoshiyuki Kitaoka (Meijo Univ.), Michihiro Nozaki (ChitaHigashi High School) A conjecture on decimal expansions of rational numbers 16:00 - 16:30 Asako Nakamura (Keio Univ.) Dirichlet's prime number theorem for PGL over function fields 17:00 - 17:30 Ryuuta Hashimoto (Nagoya Univ.) On the continued fraction of roots of trinomials 17:30 - 18:00 Kenji Nagasaka (Hosei Univ.) Sound-image processing and applied systems Friday 3 Oct. 10:00 - 10:50 Kohji Matsumoto (Nagoya Univ.) Mean values of automorphic L-functions attached to Doi-Naganuma and Ikeda lifts 11:00 - 11:50 Laurent Habsieger (CNRS France) Combinatorics and moments of L-function 13:30 - 14:00 Koichi Kawada (Iwate Univ.) On sums of cubes of primes 14:00 - 14:30 Masami Yoshimoto (Nagoya Univ. JSPS) On the square mean of L (1,c) with respect to characters 14:30 - 15:00 Hitoshi Nakada (Keio Univ.) On non-archimedean metric diophantine approximations 15:30 - 16:00 Yohei Tachiya (Keio Univ.) Irrationality of a certain Lambert series 16:00 - 16:30 Hideaki Ishikawa (Niigata Univ.) On a difference between values of L (1 2+it,cj) and L (1 2+it,ck) 2002 RIMS Conference 2001 RIMS Conference 2000 RIMS Conference 1999 RIMS Conference 1998 RIMS Conference 1997 RIMS Conference Last Modified on 08 26 2003 14:07:01 Let me know if any corrections: akiyama@math.sc.niigata-u.ac.jp
Non-commutative Aspects of Number Theory
Van Mildert College, University of Durham, UK; 28 August -- 5 September 2003.
NONCOMMUTATIVE ASPECTS OF NUMBER THEORY - Home Page NONCOMMUTATIVE ASPECTS OF NUMBER THEORY Developments and perspectives in non-commutative number theory Van Mildert College, Durham, UK 28 August - 5 September 2003 Home List of participants Summary programme Full program Abstracts Organisers: John Cremona (Nottingham) Ivan Fesenko (Nottingham) Martin Taylor (UMIST) Sponsors: GTEM AAG Programme The meeting will have two main components. The first component is a review of recent progress in areas of zeta and L functions, Langlands programme: classical and geometric, non-commutative coverings of arithmetic schemes, geometric Galois theory, non-commutative Iwasawa theory, geometric Galois module theory The second component is a review of several recent theories and approaches at changing borders between number theory and dynamical systems, non-commutative analysis, statistics, algebra, geometry, and parts of mathematical physics, which have the potential to influence future developments of number theory. The conference is primarily intended for experts in number theory, and a number of mathematicians from a range of other backgrounds will attend and actively participate in the conference. It is anticipated that the talks at the conference will be less technical and the speakers will provide a more conceptual overview of their topic. Further details accommodation information travel information confirmed participants full programme Summary programme Links to introductory texts for background reading Research Abstracts from participants The number of participants is approximately 115. 31 July 2003: registration for the conference is now closed. This conference is an official conference of the GTEM and AAG networks. Expenses for EU participants may be covered by their local nodes. For a related workshop on noncommutative geometry and number theory in Bonn, August 18-22, 2003 organized by K. Consani, Yu.I. Manin, M. Marcolli see this announcement . Material added during and after the meeting slides of talks at the conference (where available) -- updated 7 10 03 Pictures: group photos at the banquet (and after) Home List of participants Summary programme Full program Abstracts Page maintained by John Cremona (John.Cremona@nottingham.ac.uk)
Current Trends in Arithmetic Geometry and Number Theory
Banff International Research Station, Alberta, Canada; 16--21 August 2003.
Current trends in arithmetic geometry and number theory with the participation of Current trends in arithmetic geometry and number theory August 16 - 21, 2003 Organizers: Imin Chen (SFU), Brian Conrad (Univ. Michigan Ann Arbor), Eyal Goren (McGill Univ.), Adrian Iovita (Univ. Washington), Chris Skinner (Univ. Michigan Ann Arbor), Nike Vatsal (UBC) Objectives Many recent developments in number theory have relied crucially on the use of p-adic methods. These arise in many forms, such as via p-adic representation theory, p-adic L-functions, and p-adic geometry. This workshop will bring together both experts and newcomers to these areas of number theory. There will be two components to the workshop: Three lectures per day on recent developments in the field (a total of 12 lectures), consisting of various mathematicians reporting on their own work. A series of instructional lectures on $\Phi$-$\Gamma$ modules, period rings, and their applications. These lectures will be aimed at those who are not specialists in these fields, and this series will consist of 2 lectures per day (a total of 8 lectures). These will be given by Brian Conrad, Laurent Berger, Adrian Iovita, and others. The specialists in attendance are welcome to use this time for collaboration, research, and or hiking. Confirmed Participants Tentative Programme (PDF) Final Report (PDF) 2005 Banff International Research Station
Journes Arithmtiques
XXIIIrd Journes Arithmtiques. Graz, Austria; 6--12 July 2003.
XXIIIrd Journes Arithmtiques Graz 2003 XXIIIrd Journes Arithmtiques Graz 2003 July 6th - July 12th 2003
Computational Arithmetic Geometry
Sydney, Australia; 18--20 June 2003.
Workshop Computational Arithmetic Geometry, June 18 - 20, 2003, Sydney Workshop Computational Arithmetic Geometry Date: June 18 - 20, 2003. Location: Carslaw Lecture Theatre 373, Camperdown Campus, University of Sydney , Australia Description: An informal workshop, concentrating on computational arithmetic geometry and related topics. It is intended to have a relaxed schedule of talks, with ample time and opportunity for informal discussion. Programme: A preliminary programme is now available. There is also a list of abstracts . On Friday, June 20, 2pm, the workshop features the Mahler Lecture 2003: Galois Theory and Primality Testing Hendrik Lenstra Jr. (AustMS Kurt Mahler Lecturer 2003) Registration: Registration is required for participants and is free. To register, contact the organizer, preferably by email. Web page: http: magma.maths.usyd.edu.au ~bruin Workshop Poster: A poster is available in A4 format, both in postscript and in PDF format. Feel free to download and print the poster and put it on the notice board of your department. Organizer: Nils Bruin School of Mathematics University of Sydney Sydney NSW 2006 AUSTRALIA email: bruin@maths.usyd.edu.au telephone: +61 (2) 9351 4010 fax: +61 (2) 9351 4534 Scientific contributions: Participants are invited to contribute talks. I will try to accommodate all contributions, but in case of overwhelming response, I may have to make a selection. If you want to contribute a talk, please supply me with Title and Abstract. Travel: The main Campus of the University of Sydney is located 15km north of Sydney-Airport (Kingsford-Smith). The conference site can be reached by taxi (about AUD 20 -25 currently), by bus and by train . Instructions for finding the Carslaw building are available via the School Homepage . A large Campus Map is also available. Accommodation: The organization does not mediate in arranging for accommodation, but there is a list of nearby accommodations . Funding: Funds are kindly provided by MAGMA and the Computational Algebra Group , School of Mathematics , University of Sydney . A very limited amount of financial support is available towards travel and accommodation costs. This is primarily intended for graduate students and post-docs within Australia. Ask the organizer for more information. Participants: Geoff Bailey Michael Bush William Chen Claus Fieker Joost van Hamel Joseph Hammer Bill Hart Joachim Hempel David Hunt Martine Girard David Kohel Hendrik Lenstra Jr. Paul Leopardi Gerry Myerson Adrian Nelson Christopher Ormerod Loh Philip Alf van der Poorten Victor Scharaschkin Gregory Sherman Ben Smith William Stein Alexa van der Waall Paul van Wamelen Mark Watkins
Algorithms for Number Fields and Curves
Fourteenth Rencontres Arithmtiques de Caen, France; 20--21 June 2003.
Fourteenth Rencontres Arithmtiques de Caen GTEM XIVth Rencontres Arithmtiques de CAEN June 20th and 21st 2003 Algorithms for Number Fields and Curves Organizers The Rencontres Arithmtiques de Caen are organized by John Boxall and Denis Simon of the Laboratoire de Mathmatiques Nicoles Oresme, CNRS UMR 6139 at the University of Caen-Basse Normandie . Detailed schedule (with titles, abstracts, source files) About the Rencontres Arithmtiques List of the participants Registration form General Information The previous Rencontres Arithmtiques de Caen The Rencontres Arithmtiques will immediately follow the Workshop Cryptology and Algorithms in Normandy 2003 (18 and 19 June, Caen), especially devoted to lattices and cryptology. About the Rencontres Arithmtiques The Rencontres Arithmtiques de Caen have been organized during the last thirteen at the Caen University. Their goal is to review a particular aspect of number theory which is one of the research themes of the LMNO by inviting specialists on the topic. Over the years, the Rencontres Arithmtiques have become an important event for fundamental research in Normandy, and more especially in Caen. With about fifty participants and regularly edited prodeedings, they have begun to acquire an international reputation. The lectures are intended for pre- and postdoctoral students as well for more advanced researchers. Back to the top Detailed schedule of the XIVth Rencontres Arithmtiques Friday 20 June: 9h30-10h45: welcome and croissants; 11h: first lecture. Saturday 21 June: 16h: end of the last lecture. The XIVth Rencontres are devoted to the algorithms for number fields and curves. Invited speakers : K. Belabas (Universit de Paris Sud) H. Cohen (Universit de Bordeaux I) JM. Couveignes (Universit de Toulouse le Mirail) J. Cremona (University of Nottingham, England) P. Gaudry (Ecole Polytechnique) J. Guardia (Universitat Politcnica de Catalunya, Spain) M. Stoll (International University Bremen, Germany) Detailed schedule (with titles, abstracts, source files). Back to the top General Information Location of the meeting : Sciences 3 building Campus II Cte de Nacre Caen France Maps of the University Transport : A good way of coming to Caen is by train , for example for those who arrive in France at Paris. You can also fly to Caen, in which case you will arrive at the airport . To get to the Sciences 3 building from the station or the center of town, you can take the tramway (line A, to Caen Campus II). Staying in Caen : Here is a list of hotels in Caen. Please reserve a hotel yourself directly. If you stay at a hotel, please settle the bill directly with the hotel. You can also reserve a student room on Campus II. This MUST be done using the the registration form . (price 7,77 euro night for students, 11,20 euro night for other people). Reservations must be made BEFORE MAY 15. Please settle the bill directly with the residence hall on departure. Meals : Friday and Saturday lunch will be served at one of the university restaurants near the conference lecture room. On Friday evening, there will be a dinner at a restaurant, located near the port and town center. The meal will cost 40 euros. Please indicate on the registration form if you wish to attend. Registration fee : A registration fee of 25 euros is payable before the conference begins on Friday morning. The fee includes Friday and Saturday lunch. Back to the top The previous Rencontres Arithmtiques IXth Rencontres Xth Rencontres XIth Rencontres XIIth Rencontres XIIIth Rencontres Back to the top
Thematic Program on Automorphic Forms
Fields Institute, Toronto, Canada; January -- May 2003.
Fields Institute - Automorphic Forms THEMATIC PROGRAMS November17,2005 Home About Us Programs Activities Thematic Other Scientific Programs NPCDS PNSDC Commercial Industrial Mathematics Education Calendar of Events Proposals Applications Prizes Honours People Contacts Mailing List Audio Slides Publications Sponsors Fundraising Information for Visitors Mathematical Institutes Societies Search Thematic Program on Automorphic Forms January - June 2003 Clay Math Institute Summer School Audio and Slides Program Activities Graduate Courses Winter 2003 Hotels and Housing Seminars Coxeter Lecture-S. Kudla Participant List Workshops Distinguished Lecture- P. Sarnak Visitor Information Organizers: James Arthur, University of Toronto Thomas Haines, University of Maryland Henry Kim, University of Toronto Ram Murty, Queen's University George Pappas, Michigan State University Freydoon Shahidi, Purdue University Mailing List To be informed of news and updates on this program please subscribe to our mailing list at www.fields.utoronto.ca maillist Overview: The theory of automorphic forms is a wide and deep subject touching many areas of mathematics. Our purpose is to concentrate on the geometric and analytic aspects of the subject. These have far-reaching applications in classical number theory. The Langlands-Shahidi method and the converse theorem of Cogdell-Piatetski-Shapiro have seen exciting new developments recently. These include new cases of functoriality, as well as analytic continuation of symmetric power L-functions. The work of Kim-Shahidi will be one of the central themes of the program. The analytic theory of L-functions and its applications has also seen many advances in recent years. We hope to cover some aspects of these, especially those connected with the analyticity of symmetric power L-functions as well as those of Hasse-Weil zeta functions. An important problem is to express the Hasse-Weil zeta function of a Shimura variety in terms of automorphic L-functions. Here in order to define the local factors not just at primes of good reduction, we need to study the variety at the finite set of primes of bad reduction. Such a description would allow one to apply the aforementioned progress in L-functions to the study of deep arithmetic properties of these varieties. One of the major remaining obstacles to proving such a description is the so-called "fundamental lemma'' -- a conjecture in local harmonic analysis that asserts the equality of certain orbital integrals on a p-adic group and on a related (endoscopic) group. We plan to review recent work of Goresky-Kottwitz-MacPherson and others which gives a geometric approach to this problem. Coxeter Lecture Series March 10, 11, 12, 2003, 3:30 pm Stephen S. Kudla (Maryland) Arithmetic theta series Distinguished Lecture Series April 9, 10, 11, 2003, 3:30 pm Peter Sarnak (Princeton) Automorphic L-functions and equidistribution Courses: January 21 - May 1, 2003 Course on Automorphic L-functions ( Tues. Thurs., 1:30 pm- 3:00 pm) Instructors: H. Kim and R. Murty Tuesday 1:30 - 3:00 pm Course on Automorphic Functions Instructor: H. Kim Thursday 10:30 am- 12:00 pm Course on Symmetric Power L-Functions And Applications To Analytic Number Theory Instructor: R. Murty January 21- April 29, 2003, Tuesdays 10:30 am - 12:00 pm L-functions, Converse Theorems, and Functoriality for GL(n) Speaker: Jim Cogdell (Oklahoma State) Workshops: March 4-8, 2003 Workshop on Shimura varieties and related topics Organizers: T. Haines (Maryland) and G. Pappas (Michigan State) May 5-9, 2003 Workshop on Automorphic L-functions Organizers: H. Kim and R. Murty Summer School June 2-27, 2003 Clay Mathematics Institute Summer School on Harmonic Analysis, The Trace Formula and Shimura Varieties Organizers: James Arthur (Toronto), David Ellwood (Boston CMI), Robert Kottwitz (Chicago) Postdoctoral Fellowships Qualified candidates were invited to apply for postdoctoral fellowships associated with the program. Deadline for applications was January 2, 2002 Graduate Student Funding Funding is available to graduate students to visit for a term. Interested graduate students must forward a letter of application with a letter of recommendation from their supervisor. Standard support amounts for graduate students is approx. $1000 mth. If requesting travel funding please include budget outlining costs. Students should negotiate with their home institutions or advisors for additional funding if required. All documents should be received by September 30, 2002 at the following address: Thematic Program Coordinator- Automorphic Forms Graduate Student Funding, The Fields Institute 222 College Street, Second Floor Toronto, Ontario, M5T 3J1, Canada. Phone: (416) 348-9710 Fax: (416) 348-9759 Email: automorphic@fields.utoronto.ca Back to Top For more information please contact automorphic@fields.utoronto.ca
The Web of Modularity
An NSF-CBMS Conference on modular forms in Number Theory and other areas of mathematics. University of Illinois at Urbana-Champaign, IL, USA; 3--7 June 2003.
The Web of Modularity The Web of Modularity An NSF-CBMS Conference June 3-7, 2003 Department of Mathematics University of Illinois at Urbana-Champaign Many thanks to the six speakers and the 90 participants for making this meeting such a success. Schedule of talks (May be revised or updated.) All talks will be held in room 314 of Altgeld Hall. Participants (As of June 3.) Information on transportation from airport Campus map The Hendrick House is on Green St. at location 7P. The Illini Union is at location N1. Altgeld Hall is at location A14. Preliminary information for arriving participants. More complete information will be distributed at the conference registration. Important information on reimbursement for those receiving financial support Principal Lecturer: Ken Ono (University of Wisconsin) Invited Lecturers: Jan Bruinier (Cologne) YoungJu Choie (Postech) Masanobu Kaneko (Kyushu) Winfried Kohnen (Heidelberg) Ram Murty (Queen's) Registration Registration fee (to cover coffee breaks, opening reception, etc.): $35 after April 15. Please make check payable to University of Illinois, with CBMS as memo, and mail to: Scott Ahlgren, Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, IL 61801, USA. Foreign participants: you may pay $30 cash at the time of the conference. Please fill out the online registration form. Travel Participants should plan to arrive on Monday, June 2. The conference will begin on the morning of Tuesday, June 3. We will be finished on the afternoon of Saturday, June 7. See more information on transportation below. Informal Banquet On one evening we will have an informal banquet (= pizza and beverages). There may be a nominal charge for this event; please indicate whether or not you would like to participate on the registration form. Opening Reception On Tuesday evening, there will be an opening reception from 5-6:30 pm. Beer, wine, soft drinks, and light snacks will be served. Accommodations Participants are responsible for making their own arrangements. You are encouraged to make arrangements as early as possible. For the first three options listed below, please mention the CBMS Web of Modularity meeting when making a reservation. The primary facility for accommodations is the Hendrick House. This is a private guest house with inexpensive rooms, about a five minute walk from the conference site. There are two buildings: East and West. Please call early to reserve the type of room of your choice. The West Building is somewhat more modern. Prices: Single rooms: $25 per night. Double rooms: $20 per night per person. Prices for East Building: Single rooms: $21 per night. Double rooms: $17 per night per person. Parking is $3 per day. Bathrooms in both buildings are semi-private (there is one bathroom for every two rooms). Hendrick House 904 W. Green St. Urbana, IL 61801 217-365-8000 phone 217-384-4701 fax office@hendrickhouse.com The Illini Union Guest Rooms are a more upscale (and more expensive) choice. The union is next to the conference site. Rates run between $68 and $84 per night for single double rooms, with parking included. Illini Union 1401 W. Green St. Urbana, IL 61801 217-333-1241 phone iureservations@uiuc.edu A small number of rooms may also be available at the Hampton Inn (about a ten minute walk to the conference site). The rate is $60 single $65 double with parking included. Hampton Inn 1200 W. University Ave Urbana, IL 61801 Phone: (217) 337-1100 Fax: (217) 337-1143 CMIIL_Hampton@hilton.com For other possibilities in the area, see the Visitor's guide. Financial Support The application deadline has now passed, and we have distributed the funds available to us. There is a slim possibility that more funds may become available; please contact the organizers if you wish to check on this. Goals of the Conference To present an organized and motivated description of the important and diverse role which modular forms play in Number Theory and other areas of mathematics. To provide young mathematicians and newcomers to the field with an accessible account of important techniques, theorems, and open problems at the forefront of this area of research. To provide mathematicians working in areas related to the themes of the conference with an account of some areas of investigation in which their existing knowledge may prove invaluable. To provide established researchers an opportunity to share their expertise and to interact with each other and with younger mathematicians. To plan a scientific program which will lead to a published monograph of lasting importance to the wider mathematical community. Some of the topics to be considered. Introduction to Modular Forms. Arithmetic and Algebraic Interpretations of Coefficients of Modular Forms. Representation Theory of Finite Groups. Partition Theory. Gaussian Hypergeometric Series. Infinite Product Expansions of Modular Forms. Hypergeometric Series and Values of L-functions. Nonvanishing Theorems for Modular L-functions and Ranks of Elliptic Curves. Shafarevich-Tate Groups, Class groups of Quadratic fields, and Visibility. The Organizers: Scott Ahlgren and Bruce Berndt. For questions please email ahlgren@math.uiuc.edu Transportation, Parking and Maps Planes: Willard Airport (CMI) in Champaign has service from Chicago (American Airlines), St. Louis (American Airlines), and Detroit (Northwest). "Yellow" and "Corky's" shuttles meet most flights at Willard Airport, and charge $10 one-way to the Illini Union. Shuttle service from Chicago O'Hare and Chicago Midway airports (about 130 miles) and from the Indianapolis airport (about 110 miles) is available through Lincolnland Express for approximately $100 round trip. There are very good discounts for those traveling in groups of two or more. You can also obtain shuttle service from BlueBird Charters. Trains: Amtrak has daily service to Champaign from the north (Chicago) and from the south (New Orleans). From the station (the "Illinois Terminal"), catch almost any eastbound or southbound city bus ($1) or take a cab the 1 mile to the Illini Union. Automobiles: Champaign-Urbana is at the intersection of I-72, I-74 and I-57. Maps of campus and the area , including Altgeld Hall and the Illini Union . Academic Programs | Courses | ResearchAreas | People | Positions | Seminars | Publications | Library Computer Labs | Announcements | Conferences | NewsGroups | Maps | MathLinks | Search | Webmaster Department of Mathematics University of Illinois at Urbana-Champaign 273 Altgeld Hall, MC-382 1409 W. Green Street, Urbana, IL 61801 USA Telephone: (217) 333-3350 Fax (217) 333-9576 office@math.uiuc.edu
Conference in Number Theory
In honour of H.C. Williams. Banff Centre, Banff, Alberta, Canada; 24--30 May 2003.
Fields Institute - Conference in Number Theory - 2003 SCIENTIFIC PROGRAMS AND ACTIVITIES November17,2005 Home About Us Programs Activities Thematic Other Scientific Programs NPCDS PNSDC Commercial Industrial Mathematics Education Calendar of Events Proposals Applications Prizes Honours People Contacts Mailing List Audio Slides Publications Sponsors Fundraising Information for Visitors Mathematical Institutes Societies Search Conference in Number Theory in Honour of Professor H.C. Williams Saturday May 24, 2003 to Friday May 30, 2003 to be held at The Banff Centre , Banff, Alberta, Canada Sponsored by The Fields Institute, The Number Theory Foundation , RSA Security Inc. , iCore , CISaC , The University of Calgary Confirmed Attendees Schedule Manindra Agrawal Lecture Conference Proceedings Organizing Committee Michael Jacobson, Calgary Renate Scheidler, Calgary Jon Sorenson, Butler Andreas Stein, UIUC Gary Walsh, Ottawa Summary The conference is open to all areas of Number Theory, with emphasis on Computational Number Theory and applications to Cryptography. Researchers in these fields of study are welcomed to participate, as we honour Canada's foremost computational number theorist, whose contributions include results on integer factorization, primality testing, diophantine equations, linear recurrences, the infrastructure of quadratic number fields and function fields, and their applications to Cryptography. Each day of the conference will include one plenary lecture, a number of invited lectures and time has been set aside each day for contributed talks. Special Lecture Manindra Agrawal from IITK, who has recently proved the existence of a deterministic polynomial time algorithm for primality testing, will give a special evening lecture at the Banff Center on Sunday May 25, 2003, with a reception to follow in his honour sponsored by RSA Security Inc. Plenary Speakers Peter Borwein, SFU Johannes Buchmann, Darmstadt Andrew Granville, Montreal Carl Pomerance, Bell Labs Alf Van Der Poorten, Macquarie Confirmed Invited Speakers Eric Bach, Wisconsin Mike Bennett, UBC Dan Bernstein, Chicago Wieb Bosma, Nijmegen David Boyd, UBC Richard Brent, Oxford John Brillhart, Arizona Duncan Buell, South Carolina Joe Buhler, Reed College Henri Cohen, Bordeaux John Cremona, Nottingham Karl Dilcher, Dalhousie John Friedlander, Toronto Dan Gordon, CCR Jon Grantham, CCS Helen Grundman, Bryn Mawr College Mike Jacobson, Calgary Kristin Lauter, Microsoft Claude Levesque, Laval Stephane Louboutin, Luminy Greg Martin, UBC Siguna Mueller, Calgary Ron Mullin, Waterloo Attila Petho, Debrecen Richard Pinch, Cheltenham Herman te Riele, CWI Leanne Robertson, Smith College Igor Shparlinski, Macquarie Alice Silverberg, OSU Jon Sorenson, Butler Andreas Stein, UIUC Cam Stewart, Waterloo Edlyn Teske, Waterloo Sam Wagstaff, Purdue Annegret Weng, Essen Deadlines April 1, 2003- Early Registration ($200 CAD, $300 after this date) Travel and Accommodation Information **All participants are requested to make their own travel and accommodation arrangements.** To get to Banff, it is recommended that one fly to Calgary International Airport , as many Canadian, American, and overseas airlines fly to Calgary. Once in Calgary, one can get to Banff using the Banff shuttle bus . It is recommended that individuals make a reservation by web, email or phone. The shuttle bus company will provide a reduced rate to those who indicate to the airport ticket issuer that they are going to the Number Theory Conference. Rooms at The Banff Centre are limited, so those intending to book rooms are urged to do so as soon as possible. To book your room, you may print and fax this pdf file to the Banff Centre reservation office. There is considerable alternative accommodation in Banff at that time of year. Suggested activities in Banff for Conference May 24-30, 2003 Registration On-line registration is now closed. Those who want to register for the conference may do so on-site at the Banff Centre. Registration Day will be Saturday, May 24, 2003. Conference Proceedings The Fields Institute has agreed to publish the proceedings of this conference in its monograph series. A call for papers and instructions for publishing can be found here . For more information please contact numtheory@fields.utoronto.ca or Gary Walsh (gwalsh@mathstat.uottawa.ca) Back to top
The Many Aspects of Mahler's Measure
Banff International Research Station, Alberta, Canada; 26 April -- 1 May 2003.
The many aspects of Mahler's measure with the participation of The many aspects of Mahler's measure April 26 - May 01, 2003 Organizers: David Boyd (UBC), Doug Lind (Univ. Washington), Fernando Rodriguez Villegas (Univ. Texas at Austin), Christopher Deninger (Univ. Meunster) Objectives The purpose of the workshop will be to explore the many apparently different ways in which Mahler's measure appears in different areas of Mathematics. For this purpose, we are bringing together experts specializing in many different fields: dynamical systems, K-theory, number theory and topology, with the hope that common threads will emerge from the interaction between the participants. The logarithm of Mahler's measure for one variable polynomials is a quantity that occurs naturally in many problems as an entropy or grown rate. For example, it occured in Lehmer's investigation of certain cyclotomic functions and led him to ask his famous question now known as Lehmer's conjecture. In spite of fundamental work by Smyth, Dobrowolski and others on this conjecture, it has not yet been proved. Mahler's measure for polynomials in many variables was introduced by him as a device to provide a simple proof of Gelfond's inequality for the product of polynomials in many variables. It has turned out to have a much more fundamental signifigance. The starting point was the proof in the late 1970's that the Mahler measure of a several variable polynomial is the limit of the Mahler measure of one variable polynomials. The limit theorem was used by Lind, Schmidt and Ward in their proof that the logarithmic Mahler measure is the entropy of a Z^d action. Recently Deninger has shown that the Mahler measure of a many variable polynomial is related to Beilinson's higher regulators. Since then Boyd, Rodriguez-Villegas and others have explored this connection with K-theory. Some of these results can be regarded as verifications of conjectures of Kontsevich and Zagier in their general theory of periods. In another direction, connections have been found between the Mahler measure of certain two variable polynomials called A-polynomials and invariants of hyperbolic 3-manifolds such as the volume and Borel regulator. There is an intriguing conjecture of Chinburg about realizing special values of Dirichlet L-functions as logarithmic Mahler measures that seems to have a close connection to the study of the A-polynomials of arithmetic hyperbolic manifolds. We hope that most participants will give a lecture on recent work. Since the main purpose of the workshop is the interaction between individuals in different fields, we hope that the lecturers will not assume too much specialized background but will pitch their lectures to a general educated mathematical audience. In order to facilitate communication, there will be ample time for discussion which we hope will be enhanced by the beautiful setting of the workshop. Confirmed Participants Programme (PDF) Final Report (PDF) Videos click image for larger photo 2005 Banff International Research Station
Cryptographic Number Theory
Royal Holloway University of London; 4 April 2003.
Workshop on cryptographic number theory One day meeting on Cryptographic Number Theory Mathematics Department Royal Holloway University of London. Friday April 4, 2003. Public key cryptography continues to be a fertile research area on the boundary of mathematics and computer science. In particular, there is a wide range of topics in computational number theory which are directly relevant for public key cryptography. The purpose of this LMS EPSRC-funded one-day workshop was to increase the breadth of UK research in these areas. The workshop featured four one-hour research seminars by leading international experts in various areas of computational number theory cryptography. The workshop was sponsored by the London Mathematical Society and EPSRC as part of the MathFIT initiative. Lectures Slides are available by clicking on the link. Professor Gerhard Frey (Essen), Perspectives of discrete log systems, pdf file . Pierrick Gaudry (Paris), Counting points on genus 2 curves over large prime fields, ps file . Phong Nguyen (Paris), The impact of decryption failures on the security of NTRU encryption, slides not available. Igor Shparlinski (Sydney), Hidden number problem in small subgroups , ps file (4 slides on each page) . pdf file . Schedule Thursday April 3 18:00 onwards Arrival and dinner Friday April 4 9:30--10:00 Tea Coffee 10:00--11:00 Nguyen 11:00--11:30 Tea Coffee 11:30--12:30 Frey 12:30--14:00 Lunch in Athlone dining hall 14:00--15:00 Shparlinski 15:00--16:00 Tea Coffee and discussions 16:00--17:00 Gaudry 17:30 onwards Social evening at the Barley Mow Saturday April 5 11:00 onwards SECANTS 20 Links Royal Holloway University of London Royal Holloway travel information Maps of Royal Holloway SECANTS Royal Holloway Number Theory Group Royal Holloway Information Security Group Last Modified: 08-04-2003
2001 Seaway Number Theory Conference
Carleton University, Ottawa, Canada; 25--26 May 2001.
2001 Seaway Number Theory Conference 2001 Seaway Number Theory Conference School of Mathematics and Statistics Carleton University The 2001 Seaway Number Theory Conference will be held in room 4351 of the Herzberg Laboratories, Carleton University, Ottawa, Ontario, Canada on Friday May 25 and Saturday May 26, 2001. This event is sponsored by the Centre for Research in Algebra and Number Theory. In keeping with the informal nature of previous Seaway Number Theory Conferences, we will draw up the program of speakers on the morning of Friday May 25 at about 9:30 am, and we will start the first talk at 10:00 am. We expect to finish about noon on Saturday May 26. Please mark these dates in your calendar, and plan to come to the conference to give a talk on some of your work in number theory. Even if you do not wish to give a talk, please plan to come to meet your colleagues in number theory and to hear their talks. Information regarding the tentative list of speakers and titles of talks, schedule of talks , accommodation , parking and the names of those planning to attend are available below, and will be updated regularly. It would be very helpful if you would let the organizer know as soon as possible if you plan to attend and the title of your talk if you wish to speak. Please be so kind as to forward this webpage link to any colleagues and students who might be interested. Thank you and hope to see you at the conference. Kenneth S. Williams e-mail: williams@math.carleton.ca 613-520-2600 ext 2157 (office) 613-520-3536 (fax) room 4270 Herzberg Laboratories List of people planning to speak at the conference (last update May 8, 2001). Saban Alaca (Carleton University) Srinath Baba (Queen's University) Kalyan Chakraborty (Queen's University): TBA (15 minutes). Alina C. Cojocaru (Queen's University): ``Elliptic curves modulo p'' (30 minutes). J. Leslie Davison (Laurentian University): ``Some new results on continued fractions with bounded partial quotients'' (30 minutes). John Friedlander (University of Toronto) Harald A. Helfgott (Princeton University): ``The average of \mu on integers represented by a polynomial of degree greater than two and its relation to the average root number of a family of elliptic curves'' (60 minutes). Shun-ichi Katayama (Tokushima University Laval University): ``Zeta functions of finite groups and arithmetically equivalent fields'' (15 minutes). Franck Lalande (Carleton University): ``Linear relation of weight 3 between roots of polynomials'' (40 minutes). Claude Levesque (Laval University): ``On the unit group and the class number of certain composita of two real quadratic fields'' (10 minutes). Jeffrey L. Meyer (Syracuse University) M. I. Mostafa (October 6 University, Giza, Egypt): ``New identities to well-known sequences'' (15 minutes). Kumar Murty (University of Toronto) Habib Muzaffar (Carleton University) Clifford Queen (Lehigh University): ``Arithmetic on groups of positive rationals'' (50 minutes). Damien Roy (University of Ottawa) Filip Saidak (Queen's University): ``On non-abelian generalizations of the Erdos-Kac theorem, and a conjecture of Erdos and Pomerance'' (40 minutes). Abdellah Sebbar (University of Ottawa) Kotyada Srinivas (Queen's University): ``On the distict zeros of functions in the Selberg class'' (15 minutes). Drew Vandeth (University of Ottawa) Gary Walsh (University of Ottawa) Kenneth S. Williams (Carleton University, Organizer): ``The number of genera representing a given positive integer'' (10 minutes). Other participants: Boris Dekster (Mount Allison University) Larry Ericksen (Millville, New Jersey) James G. Huard (Canisius College) Daniel Panario (Carleton University) Ravi Ramakrishna (Cornell University) Program The program of talks will be finalized at 9:30 am on Friday May 25, 2001. The following is a preliminary schedule. Friday May 25, 2001 10:00am - 10:30am J. Leslie Davison 10:35am - 11:05am Alina C. Cojocaru 11:10am - 12:10pm Harald A. Helfgott 12:15pm - 12:55pm Franck Lalande 1:00pm - 2:00pm LUNCH 2:00pm - 2:50pm Clifford Queen 2:55pm - 3:10pm Kotyada Srinivas 3:15pm - 3:45pm John Friedlander 3:50pm - 4:20pm Habib Muzaffar 4:25pm - 4:55pm Abdellah Sebbar 5:00pm - 5:20pm Gary Walsh 5:25pm - 5:45pm Drew Vandeth For supper I suggest we all go out to a restaurant for 7pm. Saturday May 26, 2001 9:30am - 10:10am Filip Saidak 10:15am - 10:30am Jeffrey Meyer 10:35am - 11:05am Kumar Murty 11:10am - 11:30am Srinath Baba 11:35am - 11:55am Damien Roy 12:noon - 12:15pm Kalyan Chakraborty 12:20pm - 12:35pm Shin-ichi Katayama 12:40pm - 12:55pm Saban Alaca 1:00pm - 1:10pm Claude Levesque 1:15pm - 1:30pm Mostafa I. Mostafa 1:35pm - 1:45pm Kenneth Williams Accommodation Residence: for a room in residence on campus see http: www.carleton.ca housing tourandconf individualbookings.htm Bed and Breakfast: By-the-Way, 310 First Avenue, Ottawa, K1S 2G8, Fax Tel: (613) 232-6840. By-the-Pond, 18 Wilton Crescent, Ottawa, K1S 2T5, Tel: (613) 236-5693; Fax: (613) 236-9302. Hotel: for hotel accomomodations see http: www.ottawa.com and go to accommodations. Parking If you are planning to park your car on Carleton's campus on Friday May 25, please e-mail the organizer for a parking permit well in advance of the conference. You should park in one of the ``pay and display'' parking lots (lots P2 and P6) with your permit displayed. Otherwise, you will have to pay. A map of the campus can be found at http: www.carleton.ca cu campus . Parking is free on Saturday May 26. Address School of Mathematics and Statistics - Carleton University 1125 Colonel By Drive, Ottawa, Ontario, Canada K1S 5B6
Automorphic Forms and Applications
IAS Park City Mathematics Institute Summer Session. Park City, Utah, USA; 30 June -- 20 July 2002.
IAS Park City Mathematics Institute About PCMI Summer Session 2002 Lectures Publication Series PCMI @ MathForum Mentoring Program for Women In Mathematics ARCHIVAL MATERIAL: Mentoring Program for Women in Mathematics 2001 Summer Session 2001 Summer Session 2000 Photographs of the 1999 Summer Session Report of the 1998 Summer Session History of IAS PCMI 1994-97 IAS PCMI Summer Session 2002 Dates: June 30-July 20, 2002 Location: Prospector Square Lodging and Conference Center, Park City, Utah New: List of Confirmed Participants as of 6 3 02 New: Graduate Summer School Lecture Schedule - FINAL The flagship activity of PCMI is a three-week Summer Session. At the annual Summer Session all six of PCMIs groups high school teachers mathematics education researchers undergraduate college faculty undergraduate students graduate students mathematics researchers meet simultaneously, pursuing both individual courses of study and a meaningful amount of interaction. The rich mathematical experience combined with interaction among all participants results in greatly increased understanding and awareness of the issues confronting mathematics and mathematics education today. The Summer Session will be held in Park City, Utah, from June 30-July 20, 2002. Park City is a scenic resort town approximately 30 minutes from Salt Lake City. Long known as a popular ski resort in the winter, Park Citys summer attractions include a pleasant climate, breathtaking mountain scenery, and abundant hiking and outdoor opportunities. PCMI is a program of the INSTITUTE FOR ADVANCED STUDY, Princeton, New Jersey. Education Theme: Knowledge of Mathematics for Teaching Education Program Coordinators: High School Teachers Program Gail Burrill, Michigan State University Carol Hattan, Skyview High School, Vancouver, WA Mathematics Education Research Program International Seminar: Joan Ferrini-Mundy, Michigan State University Elementary Teaching Lab: Deborah Ball, University of Michigan Undergraduate Faculty Program Daniel Goroff, Harvard University Daniel Schaal, South Dakota State University Research Theme: Automorphic Forms and Applications Organizers of the Research Program and Graduate Summer School Peter Sarnak, Princeton University Freydoon Shahidi, Purdue University Graduate Summer School Lecturers Joseph Bernstein, Tel Aviv University Armand Borel, Institute for Advanced Study Laurent Clozel, Universite de Paris Sud Orsay James Cogdell, Oklahoma State University Alex Eskin, University of Chicago Jian Shu Li, Hong King University Wen-Ching Winnie Li, Pennsylvania State University Philippe Michel, Universite Montpellier II Zeev Rudnick, Tel Aviv University Freydoon Shahidi, Purdue University Audrey Terras, University of California San Diego Alain Valette, Universityof Neuchatel Undergraduate Program Organizers Roger Howe, Yale University William Barker, Bowdoin College Undergraduate Program Lecturers Guiliana Davidoff, Mount Holyoke College Steve Gelbart, Weizmann Institute of Science For specific information about the various programs and activities: Graduate Summer School Undergraduate Program High School Teacher Program Undergraduate Faculty Program Research Program (in Mathematics) Mathematics Education Research Program Cross Program Activities PCMI Home Page Acknowledgments Information on the Summer Session will be updated periodically. Please contact C. Giesbrecht with questions or concerns
Rational and Integral Points on Higher-dimensional Varieties
American Institute of Mathematics, Palo Alto, CA, USA; 11--20 December 2002. On-line registration.
ARCC Workshop: Rational and integral points on higher-dimensional varieties Rational and integral points on higher-dimensional varieties December 11-20, 2002 at the American Institute of Mathematics , Palo Alto, California organized by Bjorn Poonen and Yuri Tschinkel This workshop, sponsored by AIM and the NSF , will be devoted to the study of rational and integral points on algebraic varieties, primarily those of dimension at least two. We are bringing together researchers in algebraic geometry, diophantine approximation, cohomological methods (e.g. the Brauer-Manin obstruction, universal torsors), analytic methods (e.g. the circle method), and algorithmic arithmetic geometry. We hope especially to facilitate communication between researchers studying theoretical aspects and those with a more computational bent. The main questions to be addressed concern existence of points, distribution of points in various topologies, and distribution with respect to heights. The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These should be specific problems on which there is hope of making some progress during the workshop itself. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and there will be ample time between talks for discussions and for work to be done. Participants include C.L.Basile, F.Bogomolov, T.Browning, L.Caporaso, A.Chambert-Loir, J.-L.Colliot-Thlne, P.Corn, C.David, J.Ellenberg, D.Harari, B.Hassett, R.Heath-Brown, J.Johnson(tentative), A.Kresch, K.Lauter, Y.Manin(tentative), G.Matthews, B.Mazur, W.McCallum, E.Peyre, G.Rmond, F.Rodriguez-Villegas, V.Rotger, P.Salberger, P.Sarnak, A.Shlapentokh, A.Skorobogatov, W.Stein, M.Stoll, P.Swinnerton-Dyer, R.Takloo-Bighash, R.vanLuijk, A.Venkatesh, P.Vojta, J.F.Voloch, O.Wittenberg, T.Wooley, and N.Yui. The application deadline for participation in this workshop has passed. Go to the American Institute of Mathematics . Return to the AIM Research Conference Center .
The Algebraic and Arithmetic Theory of Quadratic Forms
Talca Pulcon, Chile; 11--18 December 2002.
Qudratic Forms Conference, Talca 2002 International Conference on The Algebraic and Arithmetic Theory of Quadratic Forms Instituto de Matematica y Fisica Universidad de Talca Talca, Chile December 11-18, 2002 Funded by Universidad de Talca, Conicyt The focus of the conference will be the algebraic and arithmetic aspects of quadratic forms, although related areas are also welcome. The conference will be held both at the Universidad de Talca in Talca and in Pucon, located in the lake region in the near south of Chile. Talca is a small city in the Central Valley of Chile about 260 km south of Santiago. Saturday morning the participants will travel to Pucon to resume the conference there on monday. (transportation provided). Organizing Committee Ricardo Baeza (U. de Talca) Bill Jacob (UCSB) John S. Hsia (Ohio State) Alexander Prestel (U. Konstanz) Conference Schedule: The conference opens (Talca) Wednesday evening December 11 and closes (Pucon) Wednesday morning December 18. As most international flights to Chile arrive in Santiago during the morning, participants should plan on a December 11 arrival (or earlier). This will allow for an arrival Talca by mid day with an opportunity to rest. A welcome dinner will be held Thursday evening, with talks beginning on Thursday morning. The conference will stop Saturday and Sunday. Formal sessions will resume in Pucon on Monday and Tuesday. A closing session will be held Wednesday morning December 18, allowing ample time for a return to Santiago (most international flights leave in the evening.) If possible, plan to arrive early or stay longer, as Chile has many exciting opportunities for a summer holiday this time of year. Participants: To see a partial list of participants, click here . Registration: An on-line registration form is provided for the convenience of the participants.(currently disable) Lodging: We expect that most participants will stay in a couple of Hotel's at down town Talca. The room rate is about US$ 50 per night. The number of rooms is limited, so it is important to register early. Please contact the local organizers if you need any assitance. Financial support: At this moment, we are able to provide financial support just for invited participants. Conference fee: A conference fee of US$50 (US$35 for graduates students) for non invited participants should be paid upon arrival to Universidad de Talca. Proceedings: It is intended to publish the proceedings of the conference. Getting to Talca: We have made arrangements to have a bus waiting for the incomming participants at the airport. We expect one bus to leave the airport by 11:00 AM and a van later on. Thus we encourage you to give us your arrival time in advance, so we can schedule more accurately the buses departures. If you are not able to get on any of these buses, we advise you to do the following: Upon arrival to Santiago's International airport, take a shuttle bus, "Tur Bus" which will get you to their own bus station and once in there walk a few steps and take a bus to Talca. (The same company operates both routes.) Once in Talca's bus station take a taxi to "Hotel Plaza" about $2000 (Chilean pesos) Further information: All inquiries should be addressed to the conference e-mail address: qfconference@inst-mat.utalca.cl Local Organizers: R. Baeza , M.I. Icaza , M. O'Ryan [ Photo Gallery ][ Participants ]
Function Fields and L-functions
A conference in honor of David Hayes. University of Massachusetts, Amherst, MA, USA; 15--17 November 2002.
Hayes-fest Function Fields and L-functions A conference in honor of David Hayes November 15 -- 17, 2002 University of Massachusetts, Amherst After 35 years of distinguished service at UMass Amherst, David Hayes will retire at the end of June 2002. In honor of David's many contributions to Mathematics, the Five College Number Theory Seminar will hold a meeting on November 15 (Friday) -- November 17 (Sunday). There is no registration fee for this conference. The schedule of the talks are as follow: Date Speaker Title Nov 15 4pm Benedict Gross (Harvard University) David Hayes's work on Drinfeld modules and Stark's conjecture Nov 16 9am Dinesh Thakur (Univ of Arizona) Special values of Zeta and Gamma functions Nov 16 10:30am Bruno Angles (Universit de Caen) Bernoulli type numbers and ideal class groups of Cyclotomic Function Fields Nov 16 1pm Greg Anderson (Univ of Minnesota) Kronecker-Weber plus epsilon Nov 16 2:15pm Marc Reversat (Universit Paul Sabatier at Toulouse) From positive characteristic to zero characteristic, towards a geometric correspondence for $\sigma $-difference equations Nov 16 3:45pm Cristian Popescu (Johns Hopkins) On the conjectures of Brumer-Stark and Gross Nov 17 9am Ernst-Ulrich Gekeler (Universitt des Saarlandes) Frobenius distributions of elliptic curves over finite prime fields Nov 17 10:30am Harold Stark (UCSD) p-adic Dirichlet series over quadratic fields The meeting will begin on Friday afternoon and end early afternoon on Sunday. There will be a banquet on Saturday evening. All talks will take place in Room 1634, Lederle Graduate Research Tower. Department of Mathematics Statistics, UMass Amherst. Address Directions By Air The closest airport to the UMass Campus is the Bradley International Airport in Hartford Springfield. An alternative is the Logan International Airport in Boston. By Car Driving direction and Parking information . UMass Campus Map Accomodations A block of rooms has been reserved at the UMass Campus Center Hotel . A single room is $70 per night plus tax; a double room is $80 per night plus tax. Please call 413-549-6000 or email Tina at cgray@mail.aux.umass.edu and mention "group number 747, Mathematics Statistics". November is a busy travel season here, so we urge you to make a reservation as soon as possible. If you have further questions please feel free to contact the Organizing Committee: Greg Call (Amherst College), Margaret Robinson (Mount Holyoke College), and Siman Wong (UMass Amherst).
Diophantine Problems and Analytic Number Theory RIMS Conference 2002
Research Institute for Mathematical Sciences, Kyoto University, Japan; 21--25 October 2002.
RIMS Conference 2002 Diophantine Problems and Analytic Number Theory RIMS, Kyoto University, Japan (Research Institute for Mathematical Sciences) October 21-25, 2002 *** Program *** Monday, October 21 13:00-13:05 Opening 13:10-14:00 N. Kurokawa S. Koyama : Zeta functions of higher order and their applications 14:10-15:00 A. Moriwaki : Arithmetic height functions over function fields 15:10-16:00 K. Yamanoi : Height inequalities for curves over function fields 16:10-16:40 T. Noda : Asymptotic expansions of the non-holomorphic Eisenstein series 16:50-17:20 S .Yasutomi : A remark on inhomogeneous Diophantine approximation Tuesday, October 22 9:10-10:00 D. Duverney K. Nishioka : An inductive method for transcendence of certain power series 10:10-11:00 S. Egami : Analytic continuation and the spectral resolution of a Dirichlet series 11:10-12:00 M. Bennett : Diophantine equation via Pade approximation 14:00-14:40 M. Kida : Variation of the conductor of elliptic curves under small base change 14:50-15:20 M. Higasikawa : Constructing topological groups through unit equations 15:30-16:00 T. Ishii : Explicit formulas of principal series Whittaker functions on $Sp(2, R)$ 16:10-16:40 J. Furuya : On mean values of error terms related with lattice points in hyperbolic domains 16:50-17:20 T. Komatsu : Arithmetical properties of the convergents of $e^{1 s}$ Wednesday, October 23 9:10-10:10 W. M. Schmidt : Recent developments in Diophantine approximation 10:20-11:10 R. W. Bruggeman Y. Motohashi : Embedding the Riemann Zeta-Function in $L^2(\Gamma\backslash G)$, II 11:20-12:10 K. Kawada : On sums of cubes of almost primes (free afternoon) Thursday, October 24 9:10-10:00 F. Beukers : Algebraic solutions of the Lame equation 10:10-11:00 K. Chinen L. Murata : On a distribution property of the residual order of $a$ (mod $p$), III 11:10-12:00 S. Akiyama N. Gjini : A classification of quartic Pisot tiles by their connectedness 14:00-14:40 Wenguang Zhai : On prime-independent multiplicative functions 14:50-15:20 M. Amou : Arithmetical properties of solutions of certain q-difference equations 15:30-16:00 G. Walsh : On the product of like-indexed terms in binary recurrence sequences 16:10-16:40 T. Moriyama : L-functions attached to non-holomorphic Siegel modular forms of degree 2 16:50-17:20 T. Goto : Calculation of Selmer groups of elliptic curves with a rational 2-torsion 18:00-20:00 Reception at Kyodai Kaikan Friday, October 25 9:10-10:00 M. Peter : The distribution of class numbers 10:10-11:00 K. Matsumoto : On Mordell-Tornheim multiple zeta-functions 11:10-12:10 G. Remond : Vojta's method in Diophantine geometry, applications and related topics 14:10-15:00 T. Watanabe : Hermite's constant and rational points on flag varieties 15:10-16:00 R. Okazaki : The representation of unity by quartic forms 16:10-16:50 N. Hirata-Kohno M. Huttner: Diophantine approximation of values of Gauss' hypergeometric function To find informations about RIMS, click http: www.kurims.kyoto-u.ac.jp Informations : Noriko HIRATA-KOHNO Dept. of Math., College of Science and Technology NIHON University, Kanda, Chiyoda, Tokyo 101-8308, JAPAN Back to Noriko HIRATA-KOHNO's Home Page
Number Theory Conference 96
Eger, Hungary; 29 July -- 3 August, 1996.
Conference on Number Theory 96 Welcome to the Home Page of Number Theory Conference 96 to be held in Eger, Hungary between 29th of July and 3rd of August Click here to download the registration form in TeX Click here to download the Third Announcement in LaTeX Click here to download the Call for Papers in LaTeX Click here to download the list of the titles of the talks of the participants in LaTeX The Proceedings of the conference will be published by Walter de Gruyter Co. Those participants who want to submit their paper for publication, should prepare their work in the form required by Walter de Gruyter Co. Click here to download the instruct.tex file provided by Walter de Gruyter Co., which contains detailed information about the desired format Click here to download the package of the TeX format files provided by Walter de Gruyter Co. For the convenience of the participants of the conference, we provide here the map of Eger and the map of Hungary Map of EGER Map of Hungary The e-mail address of the conference is: nt96@math.ktle.hu
Colloquium on Number Theory
In honor of the 60th birthday of Professors Klmn Gyry and Andrs Srkzy. Debrecen, Hungary; 2--7 July 2000.
Colloquium Workshop on Computational Number Theory ws2003@math.klte.hu In the frame of a scientific cooperation of Dutch and Hungarian number theorists, a workshop will be organized in the fall of this year on the subject "Computational Number Theory". It will be held from 20 to 24 October 2003 in Debrecen, Hungary. Besides the Dutch and Hungarian members of the bilateral cooperation, some experts of the field will be invited to the workshop. The main purpose of the meeting is to provide a possibility to exchange new ideas, thus to stimulate further research on this area. Therefore besides lectures, we also offer a possibility for free, informal discussions. Debrecen 20-24 October 2003 Map of the Campus Map of Debrecen List of participants List of e-mails Travel information
Explicit Algebraic Number Theory
Lorentz Center, Leiden, the Netherlands; 23 September -- 2 October 2002.
Explicit algebraic number theory September 23 - October 2, 2002 Lorentz Center , Leiden Instructional part (`Stieltjesweek'): September 23 - 26 Organizers: H.W. Lenstra , P. Stevenhagen NWO-OTKA workshop: September 27 - Oct 2 Organizers: P. Stevenhagen , R. Tijdeman Subject The title Explicit algebraic number theory is borrowed from the series of Oberwolfach meetings on Explicit methods in number theory. Those meetings are characterized by a lively interaction between abstract and advanced arithmetic theories on the one hand and concrete and elementary questions on the other. The spirit of the present workshop, which consists of 4 instructional days and 4 days of talks by (invited) participants, is similar, but within the smaller compass of algebraic number theory. Instructional part The instructional part emphasizes problems that are inspired by questions from other areas of mathematics, including elementary and algorithmic number theory, arithmetic algebraic geometry, and computer algebra. The advanced techniques from algebraic number theory that apply to these problems include class field theory, infinite Galois theory, and the theory of quadratic forms. The purpose of this part is to impart a working knowledge of these theories to the participants, to provide ample illustrations of their use, and to formulate several open problems that may be approachable by means of the same techniques. Prerequisites: basic algebra, number theory, and point set topology, including Galois theory, algebraic number theory and a knowledge of p-adic numbers. Lecturers: Hendrik Lenstra Peter Stevenhagen Bart de Smit Rene Schoof Schedule: lectures in the morning, problems and exercises in the afternoon. See the Stieltjesweek page for details. Please register on-line if you want to attend the instructional part. This will put you on the list of participants . NWO-OTKA workshop The first day of the of the NWO-OTKA workshop (friday) will try to provide illustrations of the material dealt with earlier in the week. Schedule: 4 one hour talks. The schedule on the 3 last days will be more flexible, leaving room for shorter talks and research announcements. We hope that many of our younger researchers will seize the occasion to present something here. Expected topics are explicit computations in algebraic number theory (units, class groups) and (factorization of) polynomials. Invited speakers: Yuri Bilu (Bordeaux) Jean-Marc Couveignes (Toulouse) Bas Edixhoven (Rennes) Jrgen Klners (Kassel) Gnter Lettl (Graz) Michael Pohst (Berlin) Andrzej Schinzel (Warszawa) Ren Schoof (Roma) Schedule Please register on-line if you want to attend the workshop. This will put you on the list of participants . Registered participants are entitled to free coffee and tea. Neither the Stieltjesweek nor the workshop has a registration fee. Last modified: Monday, 23-Sep-2002 18:30:41 CEST
Fermat 400 Years Later
Toulouse and Beaumont de Lomagne, France; 18--20 October 2001.
Fermat, 400 years later Fermat Historical and mathematical meeting Fermat, 400 years later Toulouse and Beaumont de Lomagne, October 18-20, 2001 Version Franaise Poster Invited speakers Program Location Registration Hotels Organization Agns Requis, Secrtariat de l' Ecole Doctorale, UFRMIG, Universit Paul Sabatier, 118 route de Narbonne, 31062Toulouse Cedex 4, France. (33) 05 61 55 82 32 (33) 05 61 55 81 74 Email : requis@picard.ups-tlse.fr
Stark's Conjectures and Related Topics
Johns Hopkins University, Baltimore, MD, USA; 5--9 August 2002. On-line registration.
Conference on Stark's Conjectures For Lecture Notes Click Here Conference on Stark's Conjectures and Related Topics Johns Hopkins University, Department of Mathematics August 5-9, 2002 A conference funded by the National Science Foundation, the Number Theory Foundation and Johns Hopkins University. Organizing Committee David Burns, King's College London, UK, david.burns@kcl.ac.uk Cristian Popescu, Johns Hopkins University, USA, cpopescu@math.jhu.edu Jonathan Sands, University of Vermont, USA, sands@math.uvm.edu David Solomon, King's College London, UK, solomon@mth.kcl.ac.uk Description of the conference In the last few years there has been a surge in research activity dedicated towards obtaining further explicit evidence for Stark's Conjecture, and in formulating and investigating natural variants, refinements or generalizations thereof. By bringing together the leading exponents of these different strands of research this conference aims to improve understanding of the links between them. In addition, the conference program will include a series of survey talks aimed at making accessible to as wide an audience as possible the main aspects of recent research into Stark's Conjecture. At this time, confirmed main speakers include. D. Burns (King's College London), H. Darmon (McGill U. ), D. Dummit (U. Vermont), M. Flach (Caltech), C. Greither (Munich), B. H. Gross (Harvard U.), D. Hayes (UMass. Amherst), M. Kurihara (Tokyo Metropolitan U.), C. Popescu (Johns Hopkins U.), K. Rubin (Stanford U.), X. Roblot (U. Lyon), V. Snaith (U. of Southampton), D. Solomon (King's College London), H. Stark(U. C. San Diego). Click on Registered Participants for a complete list of registered participants. Abstract submission deadline. Those wishing to contribute a talk are invited to submit a title and short abstract by June 15.Please send your title and abstract to the all of the following e-mail addresses: cpopescu@math.jhu.edu , david.burns@kcl.ac.uk , sands@math.uvm.edu , solomon@mth.kcl.ac.uk . Please indicate in your e-mail whether you would prefer a 30 minute slot or one of the (more limited in number) 45 or 60 minute slots. Registration. The registration deadline is June 30. In order to register, please click on the "Registration" icon to the left. There will be a $30 registration fee, to be paid on the first day of the conference. The registration fee will be waived for all the invited speakers and graduate students. Financial Support. The deadline for applications for funding is June 15. In order to apply for funding please send an e-mail message to Jonathan Sands at sands@math.uvm.edu and Cristian Popescu at cpopescu@math.jhu.edu . Lodging will be subsidized for all speakers. We also hope to be able to subsidize the travel expenses of speakers. Participation of graduate students and recent PhDs is strongly encouraged, and specific funding has been set aside to assist them. Therefore, please bring this announcement to the attention of any such individuals whom you know to be working in this or related areas. The organizers are committed to providing opportunities for women and traditionally under-represented minorities. Members of these populations who wish to attend are strongly encouraged to apply for funding.
FoCM'02 Workshop on Computational Number Theory
IMA, University of Minnesota, Minneapolis, MN, USA; 8--10 August 2002.
FoCM'02: Workshop on Computational Number Theory Workshop on Computational Number Theory Foundations of Computational Mathematics, IMA, Minneapolis, 8-10 August 2002 This is one of the 18 workshops during the conference FoCM'02 at the IMA , University of Minnesota, Minneapolis, MN, USA, 5-14 August 2002. The workshop will run for 3 successive afternoons during 8-10 August (Thursday - Saturday). Workshop organizers Dennis Hejhal (University of Minnesota; email: hejhal@math.umn.edu ) Carl Pomerance (Bell Labs; email: carlp@bell-labs.com ) Richard Brent (University of Oxford; email: Richard.Brent@comlab.ox.ac.uk ) Participants There will be fifteen 50-minute lectures during the three afternoons. The following colleagues have kindly agreed to participate: Rahul Athale (Research Institute for Symbolic Computation, Linz, Austria; email: athale@risc.uni-linz.ac.at ) Verifying the jumping champion conjecture Tim Dokchitser (University of Durham, UK; email: tim.dokchitser@durham.ac.uk ) Computing special values of motivic L-functions David Farmer (American Institute of Mathematics; email: farmer@bucknell.edu ) Calculating Maass forms Akio Fujii (Rikkyo University, Japan; email: fujii@rkmath.rikkyo.ac.jp ) Some remarks on the distribution of zeros of the Riemann zeta function Dennis Hejhal (University of Minnesota; email: hejhal@math.umn.edu ) Maass forms of CM type and quantum chaos Greg Martin (University of British Columbia; email: gerg@math.ubc.ca ) Biases in the Shanks-Rnyi prime number race Steven Miller (Princeton; email: sjmiller@math.princeton.edu ) Computers in undergraduate education and zeros of elliptic curves Mike Rubinstein (American Institute of Mathematics; email: miker@math.utexas.edu ) Computing lower order terms in the full moment conjecture for $\xi$ Harold Stark (University of California at San Diego; email: stark@math.ucsd.edu ) Siegel zeros and a new question in harmonic analysis William Stein (Harvard University; email: was@math.harvard.edu ) Verifying the full Birch and Swinnerton-Dyer Conjecture for certain specific abelian varieties Andreas Strombergsson (Princeton; email: Andreas.Strombergsson@math.uu.se ) Numerical computation of modular forms Audrey Terras (University of California at San Diego; email: aterras@ucsd.edu ) Computing Artin's L-functions of graph coverings using methods from number theory Holger Then (Ulm; email: holger.then@physik.uni-ulm.de ) Maassforms on the Picard group SL(2,Z[i]) and applications in cosmology Mark Watkins (Penn State; email: watkins@math.psu.edu ) A new database of elliptic curves Sebastian Wedeniwski (IBM Germany; email: wedeniws@de.ibm.com ) ZetaGrid - Computations connected with the verification of the Riemann Hypothesis Semi-plenary talks The talks by Greg Martin, Harold Stark and Sebastian Wedeniwski have been designated as semi-plenary, meaning that participants from other workshops are encouraged to attend them. Timetable ---THURSDAY--- ----FRIDAY---- ---SATURDAY--- 1:50-2:40 Rubinstein Strombergsson Terras 2:40-3:30 Martin Farmer Miller 4:00-4:50 Stein Wedeniwski Watkins 4:50-5:40 Fujii Then Stark 5:40-6:10 30 Athale Hejhal . Abstracts Here are the abstracts of the talks in the workshop. Links New journal by FoCM: Foundations of Computational Mathematics to the FoCM'02 page Last modified: 1st July 2002
ECHIDNA
Workshop in Arithmetic Geometry and Applications (Elliptic Curves and HIgher DimeNsional Analogues). University of Sydney, Australia; 15--19 July 2002.
ECHIDNA ECHIDNA Workshop in Arithmetic Geometry and Applications University of Sydney 15 - 19 July, 2002 General Information The Echidna workshop will focus on computational approaches in arithmetic geometry, covering arithmetic of curves, abelian varieties, and applications. The conference title signifies: Elliptic Curves and HIgher DimeNsional Analogues; or That uniquely Australian creature which follows ANTS. Registration Registration for Echidna should be indicated on the ANTS V registration page. Even if not attending ANTS, you can indicate your participation in Echidna and specify the dates of your stay from the ANTS registration page. There will be no registration fee. Accommodation Those who wish to make a reservation at the Women's College can do so together with the ANTS and Echidna registration . Other options for accomodation are available from the ANTS home page. Participants The list of registered participants is available. The programme of scheduled talks, in Carslaw 273. Contact For further information, please contact David Kohel at kohel@maths.usyd.edu.au
Analytic Number Theory
Cetraro (Cosenza) Italy; 10--19 July 2002.
Analytic Number Theory Analytic Number Theory Cetraro (Cosenza) July 10-19, 2002 Course directors: Prof. C. Viola (Universit di Pisa) viola@dm.unipi.it Prof. A. Perelli (Universit di Genova) perelli@dima.unige.it Lectures: Prof. John Friedlander Univ. of Toronto (Canada) Producing Prime Numbers via Sieve Methods (4 lectures) frdlndr@utsc.utoronto.ca Prof. John Friedlander Univ. of Toronto (Canada) Exponential Sums, Uniform Distribution and Cryptographic Applications (2 lectures) frdlndr@utsc.utoronto.ca Prof. Roger Heath-Brown Oxford University (England) Counting Rational Points on Algebraic Varieties (6 lectures) rhb@maths.ox.ac.uk Prof. Henryk Iwaniec Rutgers University, New Jersey, (USA) Automorphic L-Functions (6 lectures) iwaniec@math.rutgers.edu Prof. Jerzy Kaczorowski Poznan Un. (Poland) Axiomatic Theory of L-Functions: the Selberg Class (6 lectures) --- CIME activity is supported by Ministero degli Affari Esteri - Direzione Generale per la Promozione e la Cooperazione - Ufficio V, Ente Cassa di Risparmio, INdAM and E.U. under the Training and Mobility of Researchers Programme.
Summer School on the Birch -- Swinnerton-Dyer Conjecture
Paris, France; 4--12 July 2002.
cole d't sur la conjecture de Birch et Swinnerton-Dyer cole d't sur la conjecture de Birch et Swinnerton-Dyer PARIS, 4 - 12 juillet 2002 Organisateurs Organizers D. BERNARDI, M. HINDRY, A. KRAUS, L. MEREL Comit scientifique Scientific committee P. COLMEZ, M. HARRIS, B. KAHN, L. MEREL Cette cole est consacre aux avances, notamment les plus rcentes, en direction de la conjecture de Birch et Swinnerton-Dyer. Elle s'adresse tout mathmaticien ayant une bonne culture en arithmtique. C'est la deuxime d'une srie de quatre coles d't organise par l'Institut de mathmatiques de Jussieu. Elle amnera les auditeurs de l'nonc de la conjecture l'tude des techniques les plus sophistiques et leur donnera l'occasion de rencontrer des spcialistes de premier plan. This school is devoted to presenting progress in the direction of the Birch-Swinnerton-Dyer conjecture, with an emphasis on results obtained in recent years. It is intended for any mathematician with a good background in number theory. This is the second of four summer schools organized by the Institut de mathmatiques de Jussieu. It will lead the audience from the statement of the conjecture to the most sophisticated techniques and provide the opportunity to meet some of the best specialists in the field. Horaires Schedule Programme Program of the conference Formalits d'inscription Registration Informations pratiques Practical information Exposs en video Lectures on video
Special Activity in Analytic Number Theory
Max Planck Institute for Mathematics, Bonn, Germany; January-June 2002. Closing workshop: 24--28 June 2002.
Special Activity in Analytic Number Theory HOME GENERAL INFO PRACTICAL INFO PEOPLE DEPARTMENTS ACTIVITIES SERVICES Max Planck Institute for Mathematics, Bonn Workshop "Special Activity in Analytic Number Theory and Diophantine equations" Date: 24-28th June 2002 Place: Hrsaal, MPIM, Vivatsgasse 7 Organizers: D.R. Heath-Brown and B.Z. Moroz Programme Theme: The activity will focus on the theory of zeta-functions, prime number theory, the circle method, and the distribution of rational points on algebraic varieties. Methods from analytic number theory have brought about dramatic progress in recent years in all these areas, and inter-relationships between them are growing. It is hoped that the session will bring together researchers in these fields so as to foster such work. The session will culminate in a week long workshop, to be held 24th June 2002 to 28th June 2002. Enquiries may be addressed to the organizers: D.R. Heath-Brown rhb@maths.ox.ac.uk or B.Z. Moroz moroz@mpim-bonn.mpg.de . Proceedings of the Session `Analytic number theory and Diophantine equations' Programm for: Monday, June 24th Morning Session 09.00 - 10.00 a.m. J. Friedlander "The subconvexity problem for Artin L-functions" 10.00 - 11.00 a.m. J. Brdern "Variance estimates for the distribution of general sequences in arithmetic progressions, and almost periodic functions" 11.00 - 11.30 a.m. Coffee break 11.30 - 12.00 a.m. R. de la Bretche "Counting rational points on certain algebraic varieties" 12.00 - 12.30 p.m. J. Pintz "Linnik's approximation to Goldbach's problem" Afternoon Session 2.00 - 2.30 p.m. H. Maier "Cyclotomic polynomials, whose orders contain many prime factors" 2.30 - 3.00 p.m. A. Fujii "Some remarks on the distribution of the zeros of the Riemann zeta function" 3.00 - 3.30 p.m. M. Balazard "An approximation problem connected with the Riemann Hypothesis" 3.30 - 4.00 p.m. W. Chen "Upper bounds in the classical mean squares problem in discrepancy theory" 4.00 - 4.30 p.m. Tea break 4.30 - 5.00 p.m. A.V. Ustinov "Discrete Analogs of Bernoulli Polynomials" 5.00 - 5.30 p.m. P. Moree "The hexagonal versus the square lattice" Programm for: Tuesday, June 25th Morning Session 09.00 - 10.00 a.m. D.R. Heath-Brown "Pairs of Quadratic Forms" 10.00 - 11.00 a.m. M. Jutila "The Spectral Fourth Moment of Modular Hecke L-functions" 11.00 - 11.30 a.m. Coffee break 11.30 - 12.00 a.m. T. Wooley "Slim-stout technology: some multidimensional facets of the circle method" 12.00 - 12.30 p.m. A. Ivic "Sums of squares of the zeta-function on the critical line" Afternoon Session 2.00 - 2.30 p.m. T. Browning "Some del Pezzo surfaces of degree 5" 2.30 - 3.00 p.m. A. Sankaranarayanan "Mean-square upper bound for the Rankin-Selberg zeta-function on the critical line " 3.00 - 3.30 p.m. A. Sarkozy "Additive representation functions" 3.30 - 4.00 p.m. V.N. Chubarikov "Basis properties of arithmetical sequences" 4.00 - 4.30 p.m. Tea break 4.30 - 5.00 p.m. N.V. Kuznetsov "The fourth spectral moments of the Hecke series" 5.00 - 5.30 p.m. V.A. Bykovskii "On a computer complexity of the discrete Fourier transform" Programm for: Wednesday, June 26th Morning Session 09.00 - 10.00 a.m. Y. Motohashi "Mellin Transforms of Powers of Zeta-Functions" 10.00 - 11.00 a.m. H. Iwaniec "The Class Number Problem" 11.00 - 11.30 a.m. Coffee break 11.30 - 12.00 a.m. K. Ford "Bombieri's asymptotic sieve" 12.00 - 12.30 p.m. M. Huxley "The integer points on a smooth curve' 2.00 - 07.00 p.m. Boat trip to Knigswinter 7.30 - 12.00 p.m. Conference dinner at the restaurant "Opera" Programm for: Thursday, June 27th Morning Session 09.00 - 09.30 a.m. S. Baier "On primes close to values of a quadratic polynomial" 09.30 - 10.00 a.m. A. Skorobogatov "Combining circle method with descent" 10.00 - 11.00 a.m. J.-L. Colliot-Thlne "Values of a polynomial in one variable represented by a norm form" 11.00 - 11.30 a.m. Coffee break 11.30 - 12.30 a.m. C. Hooley "On a lower bound for the Barban-Davenport-Halberstam Sum" Afternoon Session 2.00 - 2.30 p.m. D. Tolev "Lagrange's equation with multiplicative restrictions on the variables" 2.30 - 3.00 p.m. J. Steuding "Universality for functions in the Selberg class" 3.00 - 3.30 p.m. G.I. Arkhipov "On some applications of Vinogradov's method" 3.30 - 4.00 p.m. B. Lichtin "Bounds for multivariable exponential sums mod p^r" 4.00 - 4.30 p.m. Tea break 4.30 - 5.00 p.m. R. Garunkstis "The quantitative universality theorem for the Riemann zeta-function" 5.00 - 5.30 p.m. Y. Petridis "Eisenstein series and distribution of modular symbols" 5.30 - 6.00 p.m. S. Marcello "Counting rational points in orbits of automorphisms of affine spaces" Programm for: Friday, June 28th Morning Session 09.00 - 10.00 a.m. E. Fouvry "On sign changes of Kloosterman sums" 10.00 - 11.00 a.m. P. Salberger "Counting functions in Diophantine geometry" 11.00 - 11.30 a.m. Coffee break 11.30 - 12.00 a.m. Y. Tschinkel "Rational points and automorphic forms" 12.00 - 12.30 p.m. B.Z. Moroz "On representation of primes by cubic polynomials in two variables (jointly with D.R. Heath-Brown)" Afternoon Session 2.00 - 2.30 p.m. S. Omar "Central values of a family of Artin L-functions" 2.30 - 3.00 p.m. S. Konyagin "The prime number race" 3.00 - 3.30 p.m. K. Matsumoto "On Mordell-Tornheim multiple zeta-functions" 3.30 - 4.00 p.m. S.D. Adhikari "Non-vanishing of certain infinite sums" 4.00 - 4.30 p.m. Tea break 4.30 - 5.00 p.m. A. Bege "Asymptotic formulas concerning some arithmetical functions" 5.00 - 5.30 p.m. C. Elsholtz "Some news on sums of two squares" Copyright 2004 Max-Planck-Institut fr Mathematik Impressum
XIII Meeting Rencontres Arithmtiques de Caen
Iwasawa Theory of Number Fields and Elliptic Curves. Caen, France; 20--22 June 2002.
XIII Meeting Rencontres Arithmtiques de Caen XIII Rencontres Arithmtiques Caen June 20-22, 2002 Iwasawa Theory of Number Fields and Elliptic Curves Organizing Commitee Bruno Angls( SDAD, Caen) Christian Maire (EPF, Lausanne) Alexis Michel (A2X, Bordeaux 1) Aims of the Meeting History of the Rencontres Miscellaneous About Kenkichi Iwasawa Questions? Comments? Aims of the Meeting The annual meeting of the Rencontres Arithmtiques have been organized for the last thirtheen years at the University of Caen. Each Rencontres is devoted to a specific domain of Number Theory. Thus a different topic every year, yet always in connection with the fields of research developped at the SDAD. This meeting underlines the dynanism of fundamental research in Basse Normandie and more specifically in Caen. With an average of fifty participants and proceedings edited on a regular basis, the Rencontres are now well established in the academic circle and they are doubtless to be reckoned with. The programme attracts specialists in the trade as well as doctoral students. Back to the top of the page Programme This year's topic : Iwasawa Theory for Number Fields and Elliptic Curves. Scientific Commitee : J. Coates (Cambridge University , Angleterre) R Greenberg (University of Washington Seattle,WA) T. Nguyen Quang Do (Universit de Besanon, France) B. Perrin-Riou (Universit Paris-Sud, France) Back to the top of the page History of the Rencontres IX Meeting X Meeting XI Meeting XII Meeting Back to the top of the page Miscellanous How to each Caen by train or plane How to reach us About the city of Caen The University of Caen Everything you wanted to... about the Euro Back to the top of the page About Kenkichi Iwasawa Kenkichi Iwasawa, Notices of the AMS, by John Coates Memories of Professor Iwasawa, Sugaku no Tanoshimi, by Ralph Greenberg Back to the top of the page Bruno.Angles@math.unicaen.fr Christian.Maire@epfl.ch Alexis.Michel@math.u-bordeaux.fr Back to the top of the page Last update : September 20, 2001. A.M. Anno fecit MMI Back to the top of the page Back to the department home page
Explicit Methods in Galois Theory and Arithmetic
Leiden, the Netherlands; 10--14 June 2002.
GTEM Explicit methods in Galois theory and arithmetic Midterm Evaluation Conference, Leiden, June 10-14 2002 general registration program lectures participants In the year 2000 a Research Training Network of the European Community was started under the name Galois Theory and Explicit Methods in Arithmetic . In this project 13 mathematical research institutions will have funding to cooperate for four years in order to advance knowledge in the area of inverse Galois problems, geometric Galois theory, number theory and differential Galois theory. The network sponsors postdoc positions, visiting researchers and network meetings. The Midterm evaluation meeting is organized by the Leiden team . It will take place at the Lorentz Center in the city of Leiden in the Netherlands in the period June 10-14 2002. This meeting will bring the different nodes of the network together to discuss the present state of the project. In lectures of the researchers from the various nodes we will review the results that we have obtained, and we will outline the plans for the next few years 2002-2004. On Friday, the last day of the conference, we will go through the formal "midterm review" process, where people from Brussels will evaluate the progress of the network. This part of the meeting is coordinated by Leila Schneps and Yves Andr. Last update May 27, 2002, 17:21
Tamagawa Numbers and Special Values of L-functions
Institut Galile, Universit Paris 13, France; 20--31 May 2002.
Conference on the Tamagawa number: Home
Illinois Number Theory Conference
University of Illinois at Urbana-Champaign; 17--18 May 2002.
2002 Illinois Number Theory Conference 2002 Illinois Number Theory Conference May 17 - 18, 2002 University of Illinois at Urbana-Champaign Information for Participants FIRST ANNOUNCEMENT TENTATIVE SCHEDULE OF TALKS (UPDATED 5 14 02) VENUES Altgeld Hall . The primary conference venue is Altgeld Hall, the home of the UIUC Mathematics Department. Altgeld Hall is the historic building with a bell tower, located at the southeast corner of Green and Wright Streets, next to the Illini Union, and a few blocks from Hendrick House. All talks will be given in Room 314, a large auditorium on the third floor of Altgeld Hall; for registration, coffee breaks, and Thursday's pre-conference party (see below) we will use the hallway near the north entrance to Room 314, and Room 321, the Commons Room located on the same floor opposite Room 314. Click on the above link for floor plans. Illini Union. The Illini Union is a large building adjacent to Altgeld Hall. The check-in desk for guests staying at the Union is located on the North (Green Street) side. Levis Faculty Center. Located on Illinois Street, a short walk from Altgeld Hall and Hendrick House, the Levis Center is the site of the banquet on Friday evening. Hendrick House. Hendrick House is a private student residence, located at the intersection of Green St. and Lincoln Ave., about four blocks east of Altgeld Hall. Historic Lincoln Lodge (formerly Jumer's Castle Lodge). This hotel is located on Lincoln Square, a shopping center in downton Urbana, about a 25 minute walk or a 5 minute bus ride from Altgeld Hall. To get from the hotel to the UIUC campus, simply walk west on Green Street for about 1.5 miles until you hit the intersection with Wright Street; Altgeld Hall and the Illini Union will be to your left. You can also take the "Green" bus (No. 5) which runs along Green Street. Maps and schedules are available at Champaign-Urbana public transport website . The relevant stops are Lincoln Square (for the hotel) and Green Wright (for Altgeld Hall campus). PRE-CONFERENCE PARTY Harold and Nancy Diamond will host a party on Thursday, May 16, 8 pm - 10 pm, in the Commons Room (Room 321) of Altgeld Hall. REGISTRATION Registration will be Friday, 5 17, 8:30 am - 9:00 am, in the hallway outside the Room 314 Altgeld Hall, where the lectures will be held. There is no registration fee. CONFERENCE TALKS All talks will be given in Room 314 Altgeld Hall. The room has a large blackboard, and two overhead projectors will be available. Speakers are encouraged to prepare transparencies for their talks since the blackboard may be hard to read from the back of the room. A limited number of transparencies and pens will be available at the registration desk for those who have not prepared transparencies in advance. A tentative schedule of talks is available under this link. Featured survey talks. The conference will feature three longer survey talks, covering rather different subjects, one by Harold Diamond and the other two by former students of his. We hope that these talks will appeal to a broad audience. David Bradley, Multiple polylogarithms and multiple zeta values - a survey , Friday, 8:30 - 9:20 am Harold Diamond, A survey of Beurling generlized number theory , Friday, 1:30 - 2:00 pm Jeff Vaaler, Problems and results about Mahler's measure , Saturday, 8:30 -9:20 am Contributed talks. The remaining talks have been scheduled in half hour blocks. To allow time for breaks and questions, we ask that speakers do not exeed 20 - 25 minutes. BANQUET The conference banquet will be Friday, May 17, at 6:30 pm, on the second floor of the Levis Faculty Center . Banquet tickets had to be reserved in advance, but a few extra tickets may become available due to cancellations. We are using the same caterer as last year, Classic Events Catering , which received rave reviews from conference participants. The banquet will honor Harold Diamond, who for many years has been involved in the organization of this conference and is retiring from of the University of Illinois at the end of this semester. Several of Harold's students, friends, and colleagues will give short speeches at this occasion. The banquet will offer a choice of a red meat entree (8oz strip steak), a white meat entree (grilled breast of duck), and a vegetarian entree (goat-cheese filled portabella mushroom cap). These entrees will be accompanied by rice, grilled and roasted veggies, and a salad of field greens with roasted pears, candied pecans, and crumbled gorgonzola. Desert consists of apple tarts with cinnamon ice cream, (For a more detailed - and mouth-watering - description of these items click here. ) The vegetarian entree is only available to those who had requested so on their registration form. Tickets for the two meat entrees will be distributed at registration on a first-come-first-served basis to those who have reserved a ticket. We have ordered 30 steak and 20 duck entrees, and we hope that most participants will be able to get their first choice of entree. The deadline for banquet reservations has expired; however, we will have a few extra tickets available for those who have not made reservations in advance. MEALS Continental breakfast (coffee, juice, fruit, donuts, bagels, etc.) will be available at 8:00 am on Friday and Saturday in the Commons Room of Altgeld Hall. For those staying at Hendrick House, there is a convenience store located across the street on Lincoln Ave., where coffee, (instant) cappuccino, donuts, sandwiches, and other basic food items can be purchased. Inside the Illini Union, on the first floor, is the Quad Shop, a small convenience store, and the Espresso Royale, a gourmet coffee shop. The campus area houses many restaurants and coffee shops, mostly of the fast food variety. The registration packet will include a list of restaurants in the campus area, and a map. See also the section "Maps and Visitor Information" below for a link to a listing of restaurants in the Champaign-Urbana area. AIRPORT TRANSPORTATION For participants arriving Thursday at the Champaign airport who have notified us of their travel schedule, we will try to provide transportation to the Hendrick House dormitory, the Illini Union, or the Historic Lincoln Lodge. In case we miss your arrival, or if you arrive on Friday, there is a door-to-door shuttle service which has a desk at the airport near the baggage claim area. DRIVING DIRECTIONS AND PARKING Directions to Hendrick House. From I-74, take the Lincoln Avenue exit in Urbana and proceed south for about 1.5 miles, then turn right onto Green Street. Hendrick House is the highrise building located immediately to your right at the northwest corner of Lincoln Avenue and Green Street. Those staying at Hendrick House can use the Hendrick House parking lot. Parking passes are available at the front desk, for $3 per day. All conference venues are within easy walking distance from Hendrick House Check-in procedures at Hendrick House. Guests arriving at Hendrick House during regular business hours, 8:00am-7:00pm, Monday through Friday, can check in at the front desk. Guests will be issued an entry key for the building and a key to their room. Bed linen will be laid out on the bed for the guest to make the bed upon arrival. Towels, soap and a cup are also provided. All bathrooms are shared with another guest of the same gender. The building is completely air conditioned. There is no smoking allowed. After hours check-in at Hendrick House. Guests arriving after 7 pm can gain entry by following the directions posted on the front door. A sign will be posted with the name and phone number of the resident advisor (R.A.) on duty. Use the telephone adjacent to the front door of the building to call the R.A. The R.A. will then come to the door to check you in. Directions to campus parking. Altgeld Hall and the Illini Union are located about a half mile west of Hendrick House, at the southeast corner of Green and Wright Streets. Unfortunately, parking in the campus area is very limited, and expensive, and has become more complicated because of ongoing construction work. In particular, Green Street is closed from Wright Street to Fourth Street in Champaign. (This does not affect those staying and parking at Hendrick House.) If you are staying at Hendrick House, we suggest that you leave your car at the Hendrick House lot and walk the few blocks to the conference venues. If you are staying at a motel off campus and need to park on campus, we suggest that you use the University parking garage at John and 6th Streets, located one block west of Altgeld Hall; the top floor of the garage has metered spaces (at $0.75 per hour) for visitors. Parking in the garage is free on Saturday, and after 5 pm during the week. To reach the entrance of the parking garage, we suggest the following route: Follow the directions above to Hendrick House, but continue westbound on Green Street until the next light (at Goodwin Avenue), then detour the closed part of Green St. by turning right on Goodwin Avenue, left (= west) on Springfield Ave. (which parallels Green St.), and after about half a mile turn left (= south) to Fourth Street. Cross Green Street, and take the first left, which is John Street; the parking garage is 1.5 blocks down John Street, between 5th and 6th Streets. Refer to the campus parking map for a location of parking lots. (The John Street Parking Garage is marked C7.) MAPS AND VISITOR INFORMATION Champaign-Urbana Visitor Information (This website has been down for the past few days. If the link does not work, try this one .) Maps of Champaign-Urbana (If this link does not work, try this one .) Travel directions to the University of Illinois Campus Map of the University of Illinois campus . University of Illinois Visitor Guide Champaign-Urbana Hotel Listings (If this link does not work, try this one .) University of Illinois Weather Page (with live radar picture) Champaign-Urbana weather forecast MORE INFORMATION AND CONTACT ADDRESSES Information: For more information please contact A.J. Hildebrand (ajh@uiuc.edu, 217-244-7721). Conference web page (this page): http: www.math.uiuc.edu ~hildebr nt02 . We will post updates, changes, and additional information, on this page, so please revisit the page as we get closer to the conference. Last modified Tue May 14 11:52:03 2002 ajh@uiuc.edu
L-Functions and Automorphic Forms
In honour of Joe Shalika's 60th Birthday. Johns Hopkins University, Baltimore, MD, USA; 14--17 May 2002. On-line registration.
L-Functions and Auotmorphic Forms L-Functions and Automorphic Forms Conference Johns Hopkins University, Department of Mathematics The Johns Hopkins University is sponsoring a Conference on L-Functions and Automorphic Forms in mid-May 2002, supported by the National Science Foundation, the Clay Mathematics Institute, and the JHU Department of Mathematics. May 14-17, 2002 Lectures to be held in Krieger 205 Registration be held in Krieger 209 Organizers: Arthur Jaffe, CMI Dinakar Ramakrishnan, Caltech Freydoon Shahidi, Purdue Steven Zelditch, Johns Hopkins In Honor of Joe Shalika's 60th Birthday Invited Participants (Many of Whom Will Be Speakers): William Casselman (UBC) James Cogdell (Oklahoma State U) Sol Friedberg (Boston College) Steve Gelbart (Weizman Institute, Rehovot) Masaaki Furusawa (Osaka, Japan) Thomas Hales (U Pittsburgh) Herve Jacquet (Columbia U) Dihua Jiang (Univ of Minnesota) Nicholas Katz (Princeton) Henry Kim (U Toronto) Stephen Kudla (U of Maryland) Philip Kutzko (U of Iowa) V.Lakshmibai (Northeastern U) Erez Lapid (Ohio State U) Ilya Piatetski-Shapiro (Yale) Dinakar Ramakrishnan (Caltech) Stephen Rallis (Ohio State U) Paul Sally (U of Chicago) Peter Sarnak (Princeton, NYU) Freydoon Shahidi (Purdue) Ramin Takloo-Bighash (Princeton) Yuri Tschinkel (U Penn)
Automorphic Forms and Related Topics
16th Annual Workshop. UCLA, Los Angeles, CA; 23 March 2002.
THE 16TH ANNUAL WORKSHOP ON AUTOMORPHIC FORMS AND RELATED TOPICS Preliminary List of Participants Schedule of talks WHERE: Math Sciences Bldg , UCLA, Los Angeles CA DIRECTIONS TO UCLA PARKING Lectures will be held in Math Sciences 4000a Coffee and snacks will be in Math Sciences 6620. ARRIVAL DATE: Saturday, 23 March 2002 DEPARTURE DATE: Thursday, 28 March 2002 ORGANIZERS: William Duke ( duke@math.ucla.edu ), Ozlem Imamoglu ( ozlem@math.ucsb.edu ) DESCRIPTION: Over the last 15 years, the Annual Workshop has remained a small and friendly conference. Those attending range from graduate students to well established researchers. For young researchers, the conference has provided support and encouragement; for accomplished researchers, it has provided the opportunity to mentor as well as a forum for exchanging ideas. The atmosphere is always friendly, never confrontational. The study of automorphic forms plays a central role in number theory. This conference is focused upon but not limited to automorphic forms and in fact different points of view are welcome. We anticipate that several expository lectures will be given and encourage graduate students interested in number theory to attend. GENERAL INFORMATION: As usual, there is a $25 registration fee. This money will be used to buy snacks, like fresh bagels, fruit, fresh juice, coffee and tea at breakfast time, as well as lighter snacks, coffee and tea throughout the day. In addition, your registration fee pays for your own conference coffee mug (out of which you must drink the available liquids). ACCOMODATIONS: You need to make your own hotel reservation.
Hilbert Modular Varieties and Forms
Workshop on recent developments. Far Hills Inn, near Montreal, Canada; 3--6 January 2002.
Workshop The Workshop is dedicated to surveying recent developments in the study of Hilbert modular varieties and forms, such as: (i) stratification and classification of Hilbert modular varieties, special loci and cycles; (ii) Hilbert modular forms: congruences, and associated Galois representations; (iii) Rational points on Hilbert modular varieties. Application to the Langlands program and the Fontaine-Mazur conjecture; (iv) Periods of Hilbert modular forms. Application to the construction of rational points on elliptic curves and modular abelian varieties. The workshop takes place at Far Hills Inn on January 3-6, 2002. It is financed by the Centre de Recherches Mathematiques. The number of participants is limited due to the Inn's size. Limited financial assistance is available. REGISTRATION IS CLOSED. Organizers: E. Z. Goren and H. Darmon (McGill). Location of the Workshop. Program. List of participants. Transportation. Registration. Location of the Workshop. The workshop takes place at the Far Hills Inn, located in the Laurentians, 1 hour's drive from Montreal. Transportation for people arriving January 3 and leaving January 6 will be provided by the organizers. Far Hills Inn is famous for its cross-country ski trails park, its guest services and its cuisine. Participants of the workshop will have access to all facilities, including a ski pass. Rental and ski lessons are available on location. Rates: CDN$ 88 + taxes per night, per person, based on double occupancy. CDN$ 108 + taxes per night, per person, based on single occupancy. All (three) meals (+ coffee brakes) are included in this price. Additional refreshments are not included. Far Hills Inn offers the same (very attractive) rate for spouses and for early arrival or stay after the conference. Features: The conference rooms are equipped with a blackboards, a flip chart and an overhead projector (laptop presentations are not possible). Small conference rooms for discussion are available. Bar, indoor swimming pool, sauna, cross county ski, lounge, pool table. Telephones in all rooms (internet via phone). Inn information: Web: http: www.farhillsinn.com anglais anglais.html tel: (819) 322-2014 (From Montral: (514) 990-4409, Canada and U.S.A.: 1 (800) 567-6636) fax: (819) 322-1995 address: Far Hills Inn, 3399, chemin Far Hills, Val-Morin (Qubec), Canada J0T 2R0 directions: map . Program. Thursday, January 3: 18:00-19:00 Registration 19:00 Welcome Dinner Friday , January 4 8:00-9:00 Breakfast 9:00-9:55 Henri Darmon Periods of HMF's and rational points 9:55-10:05 Coffee break 10:05-11:00 Fabrizio Andreatta Hilbert modular forms modulo p 11:30 - 13:00 Lunch Free Discussion Time 16:00-16:55 Peter Green Periods attached to objects resembling Hilbert modular varieties 16:55-17:05 Coffee break 17:05-18:00 Ed Nevens Canonical subgroups of HBAVs 18:30 Dinner Saturday, January 5 8:00-9:00 Breakfast 9:00-9:55 Fabrizio Andreatta Geometry of Hilbert modular varieties over totally ramified primes 9:55-10:05 Coffee break 10:05-11:00 Ernst Kani Modular Diagonal Quotient Surfaces 11:10-11:50 Ravi Ramakrishna Serre's conjecture and deformation theory 12:00 Lunch Free Discussion Time 16:00-16:55 Chia-Fu Yu On reduction of Hilbert-Blumenthal varieties 16:55-17:05 Coffee break 17:05-18:30 20-minutes Presentations Alex Ghitza: Sigel modular forms (mod p) and algebraic modular forms Lassina Dembele: Explicit computation of HMFs on Q(\sqrt{5}) Jeff Achter: Monodromy and abelian varieties Rachel Pries: Jacobians of wildly ramified curves 18:45 Reception Dinner Sunday, January 6 8:00-9:00 Breakfast 9:00 - 9:55 Fred Diamond Manoharmayum's proof of modularity of GL(2,F_7) representations 9:55-10:05 Coffee break 10:05-11:00 Jordan Ellenberg Modularity of two-dimensional Galois representations over F_9 11:05-12:00 Frazer Jarvis Points on Fermat curves over real quadratic fields 12:00-13:00 Lunch and Departure List of participants. J. Achter (Columbia), F. Andreatta (Padua), N. Archinard (CICMA), S. Baba (CICMA), A. Brown (Tata), H. Darmon (McGill), L. Dembele (McGill), F. Diamond (Brandeis), J. Ellenberg (Princeton), A. Ghitza (MIT), E. Goren (McGill), P. Green (Harvard), F. Jarvis (Sheffield), E. Kani (Queens), A. Logan (Berkeley), E. Nevens (Imperial College), M.-H. Nicole (McGill), U. Onn (Technion), A. Pal (CRM), A. Prasad (CRM), R. Pries (Columbia), R. Ramakrishna (Cornell), A. Saikia (CICMA), D. Savitt (CICMA), R. Sreekantan (Tata), M. Thillainatesan (Columbia), A. Tupan (CICMA), Chia-Fu Yu (Columbia). Transportation. Arrival to the workshop is on Thursday, January 3, 2002 at the afternoon, and departure on Sunday, January 6, 2002 at noon. Late arrival or early departure are not recommended. People should arrive on January 3 to McGill Mathematics Department, 805 Sherbrooke St. West, to the lounge on the 10th floor. We will depart from there by Bus at 17:00 the latest. In case of delay make every effort to inform the organizers. We shall leave the Far Hills hotel on January 6 around noon. It is highly recommended that you schedule an afternoon or night flight. Transportation will be provided from Far Hill to Dorval (and Mirabel). Registration. Registration fee (used for transportation and subsidy of the stay at Far Hills) 100$ Can. Free for students and persons without grants. Registration fee will be collected upon arrival. REGISTRATION IS CLOSED DUE TO ROOM LIMITATIONS.
Analytic Number Theory
A meeting in honour of Richard Hall. University of York, UK; 5 October 2001.
Analytic Number Theory Analytic Number Theory A meeting in honour of Richard Hall Richard Hall retired at Easter this year. The Department of Mathematics at the University of York, supported by the London Mathematical Society, is hosting a one-day meeting to celebrate Richard's mathematical work on Friday 5 October 2001, in Wentworth College, University of York. The meeting falls into the Northern Arithmetic Days series, organised by Edinburgh, Liverpool, Sheffield and York. The programme is as follows: Exhibition Area 11:00 Coffee Room W 203 11:30 Heini Halberstam: Sparse sieves 12:15 Gerald Tenenbaum: tba Exhibition Area 13:00 Lunch Room W 203 14:00 Bob Vaughan: A generalised divisor problem 14:45 Roger Heath-Brown: Arithmetic progressions of sums of two squares Exhibition Area 15:30 Tea Room W 203 16:00 Christopher Hooley: The expression of a number in the form "a_1X_1^2 + a_2X_2^2 + a_3X_3^2 + a_4W^1" 16:45 Walter Hayman: On successive zeros of the Riemann zeta function 17:30 The meeting will close, and Wentworth bar will be open. Exhibition area 19:30 Dinner There will be a registration fee of GBP10, and dinner will cost GBP20 (including wine). For further details contact Tony Sudbery at the Department of Mathematics, University of York, Heslington, York YO10 5DD (email: as2@york.ac.uk ).
Cryptography and Computational and Algorithmic Number Theory
AMS Special Session. Ohio State University, Columbus, Ohio; 21--23 September 2001.
AMS Special Session on Cryptography and Number Theory AMS Special Session on Cryptography and Computational and Algorithmic Number Theory Ohio State University, Columbus Ohio September 21-23, 2001 Pictures! Announcements Because of the recent tragic events in New York, Washington, and Pennsylvania, several of our confirmed speakers have had to cancel. The AMS has decided to go forward with the meetings, and so shall we: "We plan to go ahead with the meeting at this time and we will dedicate the meeting to mathematicians, their friends and families who have suffered from the horrible events of Tuesday 11th September." Organizers Eric Bach , University of Wisconsin at Madison, bach@cs.wisc.edu Jon Sorenson , Butler University, sorenson@butler.edu List of Speakers Daniel J. Bernstein, University of Illinois at Chicago Larry Gerstein, University of California at Santa Barbara (cancelled) Jon Grantham, IDA CCS (cancelled) Joshua Holden, Rose-Hulman Institute of Technology Michael Jacobson, University of Manitoba, Canada Jee Koh, Indiana University (cancelled) Kristin Lauter, Microsoft Corporation (cancelled) Siguna Mueller, University of Klagenfurt, Austria (cancelled) Carl Pomerance, Lucent Technologies Renate Scheidler, University of Calgary (cancelled) Oliver Schirokauer, Oberlin College Alice Silverberg, Ohio State University (cancelled) Andreas Stein, University of Illinois at Urbana Champaign (cancelled) Joe Suzuki, Osaka University (cancelled) Edlyn Teske, University of Waterloo, Canada (cancelled) Troy Vasiga, University of Waterloo, Canada Samuel Wagstaff Jr., Purdue University Gary Walsh, University of Ottawa, Canada (cancelled) Annegret Weng, University of Essen, Germany (cancelled) Hugh Williams, University of Calgary, Canada (cancelled) W. A. Zuniga-Galindo, Barry University (withdrawn) A schedule with times, titles, and abstracts in PDF is available here . (This page of information was obtained from the AMS website.) Where and When 2001 Fall AMS Central Section Meeting Columbus, Ohio, September 21-23, 2001 Meeting 969 URL: http: www.ams.org amsmtgs sectional.html Note that this is the same week as The 5th Workshop on Elliptic Curve Cryptography (ECC 2001) University of Waterloo, Ontario, Canada September 17, 18, 19, 2001 but there is a day in between, allowing attendence at both meetings. Note: The ECC meeting has been postponed to October 29th-31st. Deadlines All deadlines have passed. Registration, Accomodations, and Travel Arrangements For accommodations, travel arrangements, and registration information see http: www.ams.org amsmtgs 2059_other.html . There are special rates for several hotels near campus and on USAirways.
Higher Dimensional Varieties and Rational Points
Budapest, Hungary; 2--22 September 2001.
HIGHER DIMENSIONAL VARIETIES AND RATIONAL POINTS Alfrd Rnyi Institute of Mathematics, Budapest, Hungary, September 2 - September 22, 2001 The Alfrd Rnyi Institute of Mathematics , Hungarian Academy of Sciences which has recently been awarded the grant Centre of Excellence of the European Union, will host a 3 week programme in September 2001, in cooperation with The Erds Summer Institute, and the European networks EAGER and Arithmetic Algebraic Geometry . This event is supported by the EU High Level Scientific Conferences Project (proposal HIGHARITHM, contract No. HPCF 2001-00062). Co-chair: Jean-Louis Colliot-Thlne (Orsay) Jnos Kollr (Princeton University). Organizing Committee: Kroly Brczky, Jr. , Andrs Nmethi and Tams Szamuely . List of participants Accomodation information Arrival information Aim and scope The programme is organized in order to encourage collaboration between specialists in higher dimensional complex geometry and those studying arithmetic diophantine questions. In recent years it became apparent that the powerful geometric tools elaborated in connection with Mori's Minimal Model Program have applications over arithmetic ground fields as well. We hope that bringing together experts and graduate students specialising in higher dimensional geometry or arithmetic will induce further cross-fertilization between the two fields and give rise to new powerful results. Main topics: classification and minimal models of varieties rationally connected varieties rational and integral points fundamental groups and Galois groups Programme Week 1 (3-7 September): Instructional Conference (Euro Summer School) Schedule of lectures Abstracts of lecture courses: J.-L. Colliot-Thlne (Orsay, France): Rational points on fibrations" Abstract in dvi file Abstract in postscript file Abstract in PDF file O. Debarre (Strasbourg, France): "Fano varieties" For lecture notes, click here . Abstract in dvi file Abstract in postscript file Abstract in PDF file B. Hassett (Houston, USA): "Density of rational points on K3 surfaces and their symmetric products" Abstract in dvi file Abstract in postscript file Abstract in PDF file J. Kollr (Princeton, USA): "Rational curves on varieties" Abstract in dvi file Abstract in postscript file Abstract in PDF file S. Kovcs (Seattle, USA):"Families of varieties of general type: the Shafarevich conjecture and related problems" For slides of the lecture, click here . Abstract in dvi file Abstract in postscript file Abstract in PDF file E. Peyre (Grenoble, France): "Points of bounded height and geometry of Fano varieties" Abstract in dvi file Abstract in postscript file Abstract in PDF file Weeks 2 3 (8-22 September): Research Programme (Euro Workshop) These two weeks (8-22 September) following the Instructional Conference are mainly devoted to research work and informal discussions of a limited number of participants. There is a research seminar featuring roughly two lectures a day, usually in the morning. These are complemented by informal seminars in the afternoon, for smaller groups of participants. Ample time is left for free discussions. Programme of research seminar Funding The programme is supported by the EU Center of Excellence and High Level Scientific Conferences projects and by the Paul Erds Centre. We can cover accomodation and travel costs for selected participants. The instructional conference is agreed by the TMR network on "Arithmetic Geometry"; participants coming from a node of this network and requiring travel support should contact their local coordinator. Contact For further inquiries send an email to arithgeo@renyi.hu or contact one of the local organizers by regular mail at the following address: Alfrd Rnyi Institute of Mathematics Hungarian Academy of Sciences PO Box 127 H-1364 Budapest, Hungary Phone: (36-1) 317 3050 Fax: (36-1) 317 7166
15th Czech and Slovak International Conference on Number Theory
Topics: elementary, analytical and algebraic number theory and its applications. Ostravice, 3--8 September 2001.
International Conference on Number Theory Final announcement The 15th Czech and Slovak International Conference on Number Theory Ostravice (Czech Republic), Hotel Montr September 3. - 8., 2001 Organized by the Department of Mathematics of the Faculty of Sciences of the University of Ostrava Department of Mathematics, Institute of Chemical Technology, Prague Department of Mathematics, Masaryks University of Brno Department of Mathematical Analysis, Charles University, Prague Mathematical institute of Slovak Academy of Scientes, Bratislava PARTICIPANTS The following mathematicians confirmed the participation INVITED SPEAKERS Takashi Agoh, Japan Jannis A. Antoniadis, Greece Antal Bege, Romania Kurt Girstmair, Austria Alain Escassut, France Peter Grabner, Austria Cornelius Greither, Germany Georges Grekos, France Klman Gyory, Hungary Franz Halter - Koch, Austria Terence Jackson, United Kingdom Anatoly Karatsuba, Russia Gnter Lettl, Austria Claude Levesque, Canada Jan Min, Canada Wladyslaw Narkiewicz, Poland Jan Nekov, United Kingdom Attila Petho, Hungary Andrzej Schinzel, Poland Iliya Slavutskii, Israel Kazimierz Szymiczek, Poland PRELIMINARY LIST OF PARTICIPANTS Lubomir Alexandrov, Russia Attila Berczes, Hungary Daniel Berend, Israel Victor Beresnevich, Belarus Vasily Bernik, Belarus Michal Bulant, Czech Republic James Carter, Charleston Marzena Ciemala, Poland ALfred Czogala, Poland Ji ek, Czech Republic Cristian D. Popescu, USA Anton Deitmar, United Kingdom Ilaria Del Corso, Italy Karl Dilcher, Canada Zuzana Divisova, Czech Republic Pavla Drbkov, Czech Republic Roberto Dvornicich, Italy Vra Dvokov, Czech Republic Joseph K. Essilfie, Ghana Sophie Frisch, Austria Petr Fuchs, Czech Republic Istvn Gal, Hungary Lajos Hajdu, Hungary Jaroslav Hanl, Czech Republic Richard Hill, England Mikihito Hirabayashi, Japan Syed Furgan Ullah Hussaini, UAE Mostafa Ibrahim, Egypt Stanislav Jakubec, Slovakia Istvan Jarasi, Hungary Aleka Kalapodi, Greece Yaroslav Kholjavka, Ukraine Helmut Koch, Germany Attila Komzsik, Slovakia Petra Konen, Czech Republic Angeliki Kontolatou, Greece Juraj Kostra, Czech Republic Ella Kovalevskaya, Belarus Jan Krempa, Poland Michal Kek, Czech Republic Radan Kuera, Czech Republic Jitka Kuhnov, Czech Republic Mieczyslaw Kula, Poland Mario Lamberger, Austria Erich Lamprecht, Germany Aini Laoudi, Algerie Claude Levesque, Canada Stephane Louboutin, France Ladislav Mik, Czech Republic Ji Moko, Czech Republic Karol Nemoga, Slovakia Betislav Novk, Czech Republic Mikhail Novikov, Russia Gbor Nyul, Hungary Peter Olajos, Hungary Petr Otipka, Czech Republic Milan Patka, Slovakia Istvan Pink, Hungary Akos Pinter, Hungary Marek Pomp, Czech Republic tefan Porubsk, Czech Republic Csaba Rakaczki, Hungary Agbeko Tsikata Ransford, Ghana Thangadurai Ravindranathan, India Andrzej Rotkiewicz, Poland Selmane Schehrazad, Algeria Ladislav Skula, Czech Republic Andrzej Sladek, Poland Lawrence Sommer, USA Laszlo Szalay, Hungary Jaroslav eibert, Czech Republic John Stabakis, Greece Oto Strauch, Bratislava Herendi Tamas, Hungary Szabolcs Tengely, The Netherland Nobuhiro Terai, Japan Jrg Thuswaldner, Austria Witold Tomaszewski, Poland Jnos Tth, Slovakia Larisa Trelina, Belarus Pavel Trojovsk, Czech Republic Michal Vavros, Czech Republic Denis Vasilyev, Belarus Lev Vsevold, Israel Reinhard Winkler, Austria Takao Yamazaki, Japan PRELIMINARY PROGRAM TENTATIVE PROGRAM The conference will be opened on Monday morning, September 3rd, and finished on Saturday at noon, September 8th. Sunday, September 2nd , is the arrival day. There will be some invited plenary lectures (45 minutes) as well as contributed talks (20 minutes). Problem Section will be organized. Program in sections is only tentative. The third section might be opened. The following plenary lectures are assumed to be presented: Carter James Charleston Hilbert-Speiser number fields of given type Escassut Alain France p-adic Nevanlinna Theory and applications Grabner Peter Austria Digital function and its applications Greither Cornelius Germany Recent work on the Brumer-Stark conjecture concerning annihilation of class groups Halter- Koch Franz Austria Representation of prime powers by binary quadratic forms Jannis A. Antoniadis Greece Prime powers represented by quadratic forms Klman Gyory Hungary Bounds for the numbers of solutions of decomposable polynomial equations Karatsuba Anatoly Russia On the fractional parts of the fast increasing functions Min Jan Canada Galois, Witt and Voevodsky Narkiewicz Wladyslaw Poland Primes represented by reducible quadratic polynomials Nekov Jan United Kingdom On the parity of ranks of Selmer groups Schinzel Andrzej Poland Evaluation of a certain arithmetic sum The following titles of contributed talks have been announced till the end of June, 2001. Agoh Takashi Japan Some topics on the relative class number of cyclotomic fields Alexandrov Lubomir Russia Recurring Eratosthenes sieve and plane prime number geometry Bege Antal Romania Some inequalities concerning arithmetical functions Beresnevich Victor Belarus Diophantine approximation on curves over the field of complex numbers Bulant Michal Czech Republic On the parity o the class number of the field Q( , , , ) Corso Ilaria Italy On the index of a number field Czogala Alfred Poland Witt ring of a global field Dilcher Karl Canada Bernoulli numbers and confluent hypergeometric functions Divisova Zuzana Czech Republic On polynomial cycles in cubic fields Dvornicich Roberto Italy Bounds for the height and size of the ideal class group in CM-fields Frisch Sophie Austria On integer-valued polynomials Fuchs Petr Czech Republic Bernoulli numbers and binary trees Gaal Istvan Hungary Power integral bases in algebraic number fields Grekos Georges France Removing elements from additive bases Hill Richard England Metaplectic covers of GLn and the Gauss-Schering Lemma Hirabayashi Mikihito Japan Inkeri`s determinant for an imaginary abelian number field Jackson Terence United Kingdom An Improved bound in a problem about quaternary forms Kovalevskaya Ella Belarus p-adic variant of Khintchines theorem for the curves in Zp*Zp*Zp Koch Helmut Germany Maximal 2-extensions with given ramification points Krempa Jan Poland On completely unisotropic modules Komzsik Attila Slovakai Kek Michal Czech Republic Necessary and sufficient conditions for the primality of Fermat numbers Konen Petra Czech Republic On polynomial cycles in finite fields Levesque Claude Canada A fundamental system of units of certain fields of degree 4 over Q Louboutin Stephane France Exponents of the ideal class groups of CM number fields Lettl Gnter Austria On families of Thue equations Laoudi Aini Algerie Power integral bases in cubic cyclic number field Mostafa Ibrahim Egypt New recurrence relations to well-known sequences Nobuhiro Terai Japan On diophantine equation related to Eisenstein numbers Novikov Mikhail Russia Generalization of Bunyakovsky theorem in cases of simple and composite radicals and the applications to diophantine equations Nyul Gbor Hungary Power integral bases in biquadratic number fields Pezda Tadeus Hungary On cycles and precycles of polynomial mapping Z2 Z2 Porubsk tefan Czech Republic will be specified later Schehrazad Selmane Algeria Quadratic Extensions of Quintic Fields of Signature (3,1) Sladek Andrzej Poland Witt ring of a global field Slavutskii Iliya Israel Ankeny-Artin - Chowla conjecture: history, computation and its equivalents Somer Lawrence USA On Special Multipliers of k-th-Order Linear Recurrences Modulo pr Szalay Laszlo Hungary The diophantine equation 2n+2m+1=x2 eibert Jaroslav Czech Republic On properties and relations of some types of the numbers derived from Bernoulls inequality Trelina Larisa Belarus On the k-free factors of values of polynomials Takao Yamazaki Japan Tate duality and ramification of division algebra Trojovsk Pavel Czech Republic On properties and relations of some types of the numbers derived from Bernoulls inequality Vasilyev Denis Belarus Diophantine approximation on curves over the field of complex numbers Vavros Michal Czech Republic On polynomial cycles in the ring of circulant matrices PROCEEDINGS OF REVIEWED PAPERS The Proceedings of the conference will be published as a special issue of the journal Acta Mathematica et Informatica Universitatis Ostraviensis in 2002. The papers should be submitted in AMSTeX or another TEX format (as a file surname.TEX). The deadline for sending the paper will be on January 30, 2002. The author of a paper accepted for publication will receive a free copy of the journal and 25 free reprints. All papers submitted for publication will be reviewed. The participants will receive the detail information about this publication during the conference. CONFERENCE VENUE As it was mentioned in the first announcement, the conference will take place in a mountain centre Ostravice in a Hotel Montr. The registration office will be at the hotel Montr. TRANSPORT By plane: Participants can use domestic flights from Praque to Ostrava airport. Departures from Prague are September 2nd : 12.40, 21.40, September 3rd : 12.40, 21.40 and time of arrivals of these flights is : September 2nd : 13.40, 22.40 September 3rd : 13.40, 22.40 A transport will be organized from the Ostrava airport to the hotel Montr starting from September 2nd. By train: Participants can use any domestic or international train connection to Ostrava - Main Station. A transport from the Main Station will be organized on Sunday 2nd from 12.00 a.m. to 10.00 p.m., and on September 3rd , from. 8.00 a.m. to 2.00 p.m.. For the better organisation please let us know the time of your arrival to Ostrava-Main Station and Ostrava airport if you would like to use our transport to Ostravice. Martina.Krupova@osu.cz If you want vegetarian meals, please let us know your specific requirements to address Martina.Krupova@osu.cz By car: From Ostrava take direction of Frdek-Mstek, Frdlant nad Ostravic and Ostravice. In Ostravice, at the hotel FREUD you take direction across the railway to the mountains. Hotel MONTER is about 5 minutes by car. Hotel Monter Telephone: 00420-658-682108 Fax: 00420-658-682161 E-mail: monter@applet.cz In the hotel Monter, there are swimming pool, sauna and also masseur. There will be organized a trip (specified at the beginning of the conference, a tourist trip or visiting different places in North Moravia region). For accompanying persons a programme will be organized during the whole week. Department of Mathematics University of Ostrava 30. dubna 22 CZ-701 03 Ostrava 1 Czech Republic e-mail: Martina.Krupova@osu.cz
Arithmetic Aspects of Fundamental Groups
Euresco workshop. Acquafredda di Maratea, near Naples, Italy; 1 -- 6 September 2001.
Riemann's Zeta Function
Swiss Mathematical Society Spring Meeting. Universit de Neuchtel; 7--9 June 2001.
3me Cycle Romand de Mathmatiques SPRING MEETING OF THE SWISS MATHEMATICAL SOCIETY. 7-9 JUNE 2001 Aula Unimail Facult des Sciences Universit de Neuchtel 11, Rue Emile Argand CH-2007 Neuchtel - SWITZERLAND RIEMANN'S ZETA FUNCTION Thursday, June 7: 10.30-11.30: Andreas KNAUF (Erlangen) Probabilistic and dynamical aspects of the Riemann zeta function I. 14.15-15.15: Brian CONREY (AIM, Palo Alto) Zeros of the Riemann zeta function on the critical line. 15.45-16.45: Philippe MICHEL (Montpellier) Zeros of families of L-functions over finite fields. 17.15-18.15: Brian CONREY (AIM, Palo Alto) Moments of the Riemann zeta function. Friday, June 8: 10.30-11.30: Andreas KNAUF (Erlangen) Probabilistic and dynamical aspects of the Riemann zeta function II. 14.15-15.15: Philippe MICHEL (Montpellier) Moments of automorphic L-functions. 15.45-16.45: Henryk IWANIEC (Rutgers) Spacing zeros of L-functions on the critical line and the exceptional zero. 17.15-18.15: Peter SARNAK (Princeton Univ.) L^4 norms of eigenfunctions on arithmetic surfaces. Saturday, June 9: 11.30-12.30: Peter SARNAK (Princeton Univ.) Families of L-functions and applications. 14.30-15.30: Jean-Pierre BOURGUIGNON (CNRS-IHES) Geometry under Physics' influence. Information concerning hotels and other accommodations can be found here . Contact person: Alain Valette Institut de Mathmatiques 11 Rue Emile Argand CH-2007 Neuchtel - Switzerland e-mail: alain.valette@unine.ch Back to the previous page.
Research Experiences for Undergraduates in Number Theory
University of Illinois, Urbana-Champaign; 11 June -- 3 August 2001.
REU - Undergraduate Research Experiences for Undergraduates, Mathematics Research Experiences for Undergraduates (REUs) 2005 Summer REUs , funded by a National Science Foundation (NSF) Workforce in the Mathematical Sciences Program . Past REUs held by the Department , funded by a National Science Foundation (NSF) Vertical Integration of Research and Education (VIGRE) grant. Last modified February 21, 2005
The Dwork Trimester
A cycle of conferences in honour of B. M. Dwork. Italy; May--July 2001.
A cycle of conferences on Dwork Theory Remembering Bernie The Dwork Trimester in Italy May--July2001 The Organizing Committee of the Dwork Trimester wishes to thank all those who participated for their contributions to the success of this scientific memorial to Bernie. Sites of the Conference Tentative Schedule Dwork' page of the Rendiconti Scientific Committee: Alan Adolphson Francesco Baldassarri Pierre Berthelot Gilles Christol Nicholas Katz Franois Loeser Steven Sperber The following mathematicians are expected to participate: A. Adolphson Y. Andr F. Baldassarri L. Berger V. Berkovich P. Berthelot J.-B. Bost J.-F. Boutot B. Chiarellotto G. Christol R. Coleman P. Colmez R. Crew A. D'Agnolo H. Darmon L. Di Vizio M. Emerton J.-Y. tesse E. Goren H. Hida Ch. Huyghes L. Illusie N. Katz K. Kedlaya M. Kisin B. LeStum F. Loeser F. Maaref S. Matsuda B. Mazur W. Messing F. Mokrane A. Ogus B. Perrin-Riou L. Ramero C. Sabbah P. Schapira P. Schneider S. Sperber H. P. F. Swinnerton-Dyer J. Tate T. Terasoma J. Tilouine N. Tsuzuki I. Vidal A. Virrion N. Wach D. Wan The primary goal of the conference is the investigation of the intrinsic geometric content of the arithmetic results and of the p-adic analytic methods due to Bernard Dwork (New York 5 27 1923 - Princeton 5 9 1998). Dwork exerted a strong influence on contemporary algebraic geometers with his proof of rationality of the zeta function of an algebraic variety over a finite field, and the introduction of a completely new p-adic cohomology theory for hypersurfaces of characteristic p 0. He produced deep p-adic results on the Hodge structure of Picard-Fuchs equations and founded a general theory of p-adic differential equations. Rather than a collection of isolated and ingenious methods enabling the proofs of some very deep theorems in arithmetic, Dwork's theory and results have great internal cohesion and are intimately and intrinsically related to the algebraic-geometric approach of Grothendieck and his school. It is the goal of this conference to explore these connections and to present new developments in Dwork's theory via a collection of main lecture cycles dedicated to some of the most important aspects of the theory. The most welcome listeners would be, besides specialists, young post-docs and graduate students in Arithmetic Algebraic Geometry. This extended period of work will include two special events. These will be one-week conferences on p-adic modular forms, p-adic L-functions and p-adic integration organized by M. Bertolini ( massimo@dimat.unipv.it or massimo@math.unipd.it ), to be held in Villa Monastero in Varenna on Lake Como from Sunday, June 3 to Saturday, June 9, 2001. (The lectures will be held from the morning of Monday, June 4 to Friday afternoon, June 8) Geometric Aspects of Dwork's Theory to be held in Bressanone, from Sunday July 1 to Saturday July 7, 2001. We expect to produce a volume of Proceedings. This activity will be co-sponsored by the Istituto Nazionale di Alta Matematica (INdAM), Rome, and by the European Network ``Arithmetic Algebraic Geometry''. The conference will be of course open to more specialized and or informal contributions. For further information, watch this page or contact F. Baldassarri at baldassa@math.unipd.it
Galois Modules in Arithmetic Geometry
Part of the 2001 Arithmetic Semester in Lille. It will immediately follow the Journes Arithmtiques. Lille, France; 9--13 July 2001.
GaMAG GaMAG GaloisModule in ArithmeticGeometry July 9-13, 2001 Aims of the conference Foster the systematic study of Galois module structure by means of tools and methods developed in arithmetic algebraic geometry. This conference is aimed at researchers in the field whom it offers an overview of the subject and an opportunity to meet and at researchers in nearby fields to whom it offers potential applications of techniques they are acquainted with. There will be two kinds of lectures : - mini-courses or morning tlak series, which summarize results and techniques that lay at the foundation of recent approaches (see below) - individual lectures on the state-of-the-art (see the on-line programme below for the complete list) Morning Talk Series A Beilinson's conjectures Four Lectures byJ. Nekovar (Cambridge, UK) B I wasawa Theory Applicable to the Subject a) Iwasawa theory and cohomology Three Lectures by C. Greither (Munich, D) b) Iwasawa theory and special values of L-functions Three Lectures byD. Benois (Bordeaux, F) C Recent results in Galois Module Structure a) Coherent Euler characteristics and Galois module structure Three Lectures by T. Chinburg (Penn, Philadelphia, USA) b) Application of the Deligne-Riemann-Roch theorem One Lecture by M. J. Taylor (UMIST, UK) Afternoon Talks A Around Stickelberger: J. Lee, C. Popescu, V. Snaith B Explicit Structures: J. Fowler, G. Elder, N. Byott, H. Gangl C Iwasawa or p-adic representations in play: A. Agboola, J. Ritter, A. Weiss D Equivariant Bloch-Kato and Riemann-Roch: N. Borne, W. Bley, M. Flach The GaMAG leaflet C. Greither's talk series T. Chinburg's talk 1 T. Chinburg's talk 2 T. Chinburg's talk 3 M. Taylor's talk This event is jointly organized by the universities of Bordeaux I , Lille I and Valenciennes with the financial support of GDR de Thorie des Nombres A2X de Universit Bordeaux 1 AGAT de Universit Lille 1 Lamath de l'Universit Valenciennes Journal de Thorie des Nombres de Bordeaux GTEM European Network For further information Philippe Cassou-Nogus (Bordeaux 1) phcassou@math.u-bordeaux.fr Boas Erez (Bordeaux 1) erez@math.u-bordeaux.fr Alexis Michel (Bordeaux 1) michel@math.u-bordeaux.fr This page will be regularly updated Last update July, 15 2001 A. M. anno fecit MMI
Gomtrie Algbrique et Applications Arithmtiques
A conference in honour of Michel Raynaud. On-line registration. Orsay, France; 18--22 June 2001.
Version FR English version GOMTRIE ALGBRIQUE ET APPLICATIONS ARITHMTIQUES CONFRENCE EN L'HONNEUR DE MICHEL RAYNAUD ORSAY, 18-22 juin 2001 Btiment 452, amphi. F2 Confrenciers invits Ahmed Abbes, John Coates, Gerd Faltings, David Harbater, Yasutaka Ihara, Johan de Jong, Nicholas M. Katz, Barry Mazur, Vikram. B. Mehta, Laurent Moret-Bailly, Frans Oort, Michael Rapoport, Kenneth A. Ribet, Jean-Pierre Serre, Christopher Skinner, Tetsuji Shioda, Akio Tamagawa, John Tate. Programme Comit d'organisation Jean-Benot Bost Luc Illusie Jean-Marc Fontaine Yves Laszlo Grard Laumon Information : mr2001@math.u-psud.fr Vous trouverez aussi une liste d'htels sur le web. Les mathmaticiens projetant d'assister la confrence sont pris de bien vouloir remplir le formulaire d'inscription , mme s'ils rsident en rgion parisienne.
Arithmetic Geometry
A special session of the BMS DMV joint meeting. Liege, Belgium. 8--10 June, 2001.
Private Homepage -- Kurzinfos Private homepages like http: www-physik.uni-regensburg.de ~dau12345 do not exist any longer! You find all private homepages of the University using the URL http: homepages.uni-regensburg.de ~ user-id Private Homepages in der zentralen Unixdomne Stand 14.11.2001 Fritz Wnsch Rudolf Holzer Da der Physik-eigene WAP Server demnaechst abgeschaltet wird, kann es auch keine privaten Homepages der Form http: www.physik.uni-regensburg.de ~ user-id mehr geben. Die privaten Homepages in der zentralen Unixdomaine haben die Adresse http: homepages.uni-regensburg.de ~ user-id und liegen im CIP-Datenbereich im Subdirectory public_html. Bitte sorgen Sie dafr, da die Recht auf dieses Verzeichnis korrekt gesetzt sind, nmlich drwxr-xr-x 3 dau08015 phy 512 Mar 28 2001 public_html F Inhalt und Links der privaten Seiten ist ausschlielich der Ersteller verantwortlich!!. Die Fakultt Physik distanziert sich ausdrcklich von Links und Inhalten dieser Seiten. Sie sind privater Natur und geben nur die Meinung des Autors wieder. Eine Liste der privaten Homepages der Universitt gibt es hier .
Workshop on Hodge Theory, Galois Theory, Moduli and Arithmetic Geometry
Kyoto University, Japan; 21--24 May 2001.
Second announcement on Workshop on Hodge theory, Galois theory, moduli and arithmetic geometry Workshop on Hodge theory, Galois theory, moduli and arithmetic geometry Second Announcement, completed on Apr. 20th 2001 Return to Matsumoto's home page May 21st-24th, 2001 at Kyoto University, Graduate School of Human and Environmental Studies Professor Richard Hain at Duke University will visit Kyoto Univerisity during May 15--June 4. Taking this opportunity, we would like to have a workshop on the closely related areas in mathematics: moduli spaces of curves, mapping class groups, (usual and p-adic) Hodge theory, Galois theory, motives, K-theory, iterated integrals, modular forms, etc. Date: May 21st(Mon.) -- 24th (Thu.), 2001 Place: Kyoto University, Graduate School of Human and Environmental Studies Room No. G226 Access and Map Confirmed speakers include: Toshiyuki Akita (Hokkaido Univ.) Masanori Asakura (Kyushu Univ.) Kenichi Bannai (Univ. Tokyo) Hidekazu Furusho (RIMS) Richard Hain (Duke Univ.) Kazuya Kato (Univ. Tokyo) Nariya Kawazumi (Univ. Tokyo) Makoto Matsumoto (Kyoto Univ.) Shinichi Mochizuki (RIMS) Sigeyuki Morita (Univ. Tokyo) Takayuki Oda (Univ. Tokyo) Shuji Saito (Nagoya Univ.) Tomohide Terasoma (Univ. Tokyo) (Click the name for the title and the abstract of the talk.) Tentative plan of the schedule of the talks For more information, please contact to: Makoto Matsumoto (email: matumoto@math.h.kyoto-u.ac.jp ) Kyoto Univ., Faculty of Integrated Human Studies. Sakyo-ku Kyoto 606-8501 JAPAN. Tel: +81-75-753-6754 Fax: +81-75-753-6767
Illinois Number Theory Conference 2001
University of Illinois at Urbana-Champaign; 18--19 May 2001.
2001 Illinois Number Theory Conference 2001 Illinois Number Theory Conference and Workshop on the Interface of Probability and Number Theory May 18 - 20, 2001 University of Illinois at Urbana-Champaign First announcement Schedule of talks REGISTRATION Registration for the Illinois Number Theory Conference and the Probability Workshop will be Friday, 5 17, 8:30 am - 9:00 am, outside the lecture room, 314 Altgeld Hall. There is no registration fee. TALKS All talks will be given in Room 314 of Altgeld Hall , the building housing the UIUC Mathematics Department. Altgeld Hall is the historic building with a bell tower at the southeast corner of Green and Wright Streets. Altgeld Hall is adjacent to the Illini Union , about a third of a mile west of Hendrick House (along Green Street), and about half a mile south of the Hampton Inn (along Wright Street, or across the "Engineering Quad"). Invited talks: The conference will feature two hour-long survey talks: Vishwa Dumir (UIUC and Panjab University), View obstruction problems: a survey. Friday, 5 18, 9:00 am - 9:50 am Doug Bowman (UIUC), Multiple zeta values: a survey. Friday, 5 18, 1:30 pm - 2:20 pm Contributed talks: Contributed talks have been scheduled in 25 minute blocks, to allow for a 5 minute break between talks. Please adhere to the 20 minute limit for contributed talks in order to keep the schedule on track. TRANSPARENCIES We encourage speakers to prepare transparencies for their talks, since the blackboard is hard to read from the back of the room. Two overhead projectors will be available. A limited number of transparencies and pens will be available at the registration desk for those who have not prepared transparencies in advance. BANQUET The conference banquet will be Friday, May 18, at 6:30 pm, in Room 407 of the Levis Faculty Center , located on Illinois Street, about a third of a mile east of Altgeld Hall. Banquet tickets had to be reserved in advance, but a few extra tickets may become available due to cancellations. The banquet will offer a choice of two meat entrees (steak and turkey), and a vegetarian (Vegan) entree (eggplant). The vegetarian entree had to be prereserved. The two meat entrees have been ordered in equal numbers. Banquet tickets will be given out at registration; the tickets will be color coded according to the entree choice. The tickets will be collected by the wait staff, so be sure not to lose your tickets. MEALS The campus area houses many restaurants and coffee shops, mostly of the fast food variety. The registration packet will include a list of restaurants in the campus area, and a map. See also the section "Maps and Visitor Information" below for a link to a listing of restaurants in the Champaign-Urbana area. AIRPORT TRANSPORTATION For participants arriving Thursday at the Champaign airport who have notified us of their travel schedule, we will provide transportation to the Hendrick House dormitory, the Hampton Inn, or the Illini Union. In case we miss your arrival, or if you arrive on Friday, there is a door-to-door shuttle service which has a desk at the airport near the baggage claim area. Those staying at the Hampton Inn can use the free hotel shuttle service provided by the hotel; call the hotel from the airport to request the shuttle. Transportation back to the airport on Sunday will be arranged during the conference. DRIVING DIRECTIONS AND PARKING From I-74, take the Lincoln Avenue exit in Urbana and proceed south on Lincoln Avenue for about 1 1 2 miles to the traffic light on Green Street, then turn right. Hendrick House is the highrise building located immediately to your right at the northwest corner of Lincoln Avenue and Green Street. Altgeld Hall and the Illini Union are located about a half mile further down Green Street, at the southeast corner of Green and Wright Streets. Parking in the campus area is very limited; if you need to park on campus, we suggest you use the University parking garage at John and 6th Streets, located one block west of Altgeld Hall; the top floor of the garage has metered spaces for visitors. The meters are in effect on Friday; parking is free on Saturday at the University garage and on other University lots; refer to the campus parking map for location of parking lots. An alternative to the parking garage is the attended municipal parking lot at the northwest corner of 6th and Wright Streets. Note, however, that municipal parking is not free on Saturday. The Hampton Inn offers free parking for its guests. The parking lot at Hendrick House is closed for renovation, but guests at Hendrick House can park for $2.50 per day at Unversity Lot D9, located at the southwest corner of the intersection of Green and Lincoln, directly across from Hendrick House; this map shows the exact location. Permits can be purchased at the Hendrick House reception desk. MAPS AND VISITOR INFORMATION Map of Champaign-Urbana Travel directions to the University of Illinois Campus Map of the University of Illinois campus . Campus parking map Champaign-Urbana Visitor Information University of Illinois Visitor Guide Restaurant Listings Champaign Hotel Listings Urbana Hotel Listings University of Illinois Weather Page (with live radar picture) Champaign-Urbana weather forecast MORE INFORMATION AND CONTACT ADDRESSES Organizing Committee: Harold Diamond (diamond@math.uiuc.edu) and A.J. Hildebrand (ajh@uiuc.edu). Please feel free to contact one of us if you have questions. Conference web page (this page): http: www.math.uiuc.edu ~hildebr nt2001 . We will post updates, changes, and additional information, on this page, so please revisit the page as we get closer to the conference. Last modified Sat May 26 08:57:31 2001 ajh@uiuc.edu
Workshop on the Interface of Probability and Number Theory
University of Illinois, Urbana-Champaign, USA; 19--20 May 2000. Abstracts.
Workshop on the Interface of Probability and Number Theory Workshop on the Interface of Probability and Number Theory Millennial Conference Homepage Abstracts of Talks (postscript file) Schedule of Talks (updated 5 19 2000) Scientific Program This two day workshop is part of the Special Year in Number Theory 1999 2000 , and a satellite conference to the Millennial Conference on Number Theory , which is held during the week following the workshop. Its purpose is to bring together researchers from the probability and number theory communities interested in problems that lie at the interface of these two areas. The themes of the workshop include: Probabilistic number theory Uniform distribution and discrepancy Probabilistic methods in additive number theory Probability theory on algebraic and combinatorial structures Probabilistic models in number theory Speakers R. Arratia (Univ. of Southern California) G.J. Babu (Penn State Univ.) W. Chen (Macquarie Univ.) J.-M. Deshouillers (Univ. of Bordeaux) M. Drmota (Technical Univ. of Vienna) P.D.T.A. Elliott (Univ. of Colorado) A. Granville (Univ. of Georgia) M. Kolountzakis (Univ. of Crete) E. Manstavicius (Vilnius Univ.) H. Montgomery (Univ. of Michigan) J. Schoissengeier (Univ. of Vienna) G. Tenenbaum (Univ. of Nancy) R. Tichy (Technical Univ. of Graz) M. Yor (Univ. of Paris VI) V. Vu (Microsoft Research) Venue All talks will be given in Room 245 Altgeld Hall. Altgeld Hall is located about 4 blocks east of the Quality Hotel where most participants are staying. To reach Altgeld Hall from the Quality Hotel, walk 4 blocks east on John Street until you come to the end of this street when it meets Wright Street. Altgeld Hall is the historic building with a small bell tower at the other side of Wright Street. Signs with directions to the lecture room will be posted. The Levis Faculty Center, where the Reception on Saturday evening will be held, can be reached by walking the equivalent of about 3 blocks east from Altgeld Hall, crossing Matthews and Goodwin Avenues. Maps will be provided with the registration packet. For additional information, maps, and directions, visit the Conference Venue section of the Millennial Conference homepage. Registration Registration for this workshop will be Friday morning, 8:30 am - 10:00 am, in the lobby of the main floor of Altgeld Hall. Participants will receive a folder with a conference program, list of abstracts, maps, and a name tag. Registration for the workshop is free. If you are planning to stay over for the Millennial Conference on Number Theory (May 21 - 26, 2000), you can register for that conference Saturday, 3 pm - 5 pm or on Sunday morning. Lectures All talks will be given in Room 245 of Altgeld Hall. Although the room has a large blackboard, we recommend that speakers use transparencies. The room is equipped with two overhead projectors. Transparencies and pens will be available at the registration desk for those who have not prepared their transparencies in advance. Reception A reception for participants at the Millennial Conference on Number Theory, which begins Sunday, May 21, will be given on Saturday, May 20, from 8 - 10 pm, in the Levis Faculty Center, located a few blocks east of Altgeld Hall. All workshop participants are invited to attend this reception. For maps and directions to the Levis Faculty Center, see the Conference Venue section of the Millennial Conference homepage. Travel Most participants will be staying at the Quality Hotel. The hotel has a free shuttle service to and from the Champaign airport. When you arrive at the airport, call the hotel at 384-2100 or tollfree at 800-322-8282 to request the shuttle. (Note that the Quality Hotel does not have a courtesy phone; you need to use one of the pay phones located near the baggage area.) The trip from the airport to the Quality Hotel takes about 15 minutes. Accommodations Participants of the workshop will have the same lodging options as the the participants of the Millennial Conference following the workshop: a hotel and a student dormitory, both located within a few minutes walk from the conference site. Room reservations must be made directly with the hotel or the University housing service, and not with the conference organizers. The rooms have been blocked for the period May 18 - May 29, which covers both the Millennial Conference on Number Theory and its two satellite conferences. When making hotel or dormitory room reservations, please identify yourself as a participant of the "Number Theory Conference", rather than this workshop. This will ensure that you receive the special conference rate; it does not obligate you to stay for Millennial Conference. If you have difficulties making reservations yourself, let us know and we will try to make the reservations for you. Hotel accommodation: We have reserved a block of rooms at the Quality Hotel - University Center, 302 E. John St., Champaign. This hotel, located a few blocks from the University campus, is a 20 story high rise building with large and comfortable rooms, many of which offer a great view of the University campus and the cities of Champaign-Urbana. The hotel was formerly known as the University Inn, but is now part of the Quality Inn hotel chain. The rates for conference participants are $50 per night for a single room and $62 per night for a double room, plus 11% tax. Reservations should be made directly with the hotel, by calling the hotel at 800-322-8282 or 217-384-2100, sor sending your request by fax to 217-384-2298. When making the reservation, please identify yourself as a participant of the "number theory conference" in order to obtain the special conference rate. The deadline for reservations is April 20, 2000; after that date, the rooms will be released and may no longer be available. Dormitory accommodation: We have also reserved rooms at the Busey-Evans Halls, 1111-1115 W. Nevada, Urbana, two connected buildings on the University campus, which are used as student dormitories during the semester and as housing for conference guests during semester breaks. These residence halls are among the nicest on the UIUC campus and are fully airconditioned. Conference guests have a choice of single rooms at approximately $30 per night and double rooms at approximately $20 per night and per person. (These are estimated rates for Summer 2000, and do not include tax; final rates have not yet been set.) The rooms will have sheets, blankets, pillows, and towels, and there will be daily exchange of towel and washcloth. Bathroom facilities are single sex and centrally located on each floor. Each room has free local phone service, guests may use a calling card to outgoing toll calls and can receive calls directly to their room phone. To make reservations, call the Housing - Conference Services at 217-333-1766, or use the online reservation form at http: www.housing.uiuc.edu conference millennial.html . The deadline for making reservations is April 18, 2000. Contact addresses Organizers: A.J. Hildebrand, Dept. of Mathematics, Univ. of Illinois, Urbana, IL 61801, USA, email ajh@uiuc.edu W. Philipp, Dept. of Statistics, Univ. of Illinois, Urbana, IL 61801, USA, email wphilipp@uiuc.edu Conference web page (this page): http: www.math.uiuc.edu nt2000 probability Last modified Tue May 30 15:33:24 2000 ajh@uiuc.edu
Unusual Applications of Number Theory
DIMACS, Rutgers University, Piscataway, NJ, USA; 10-14 January 2000.
DIMACS Workshop on Unusual Applications of Number Theory DIMACS Workshop on Unusual Applications of Number Theory January 10 - 14, 2000 DIMACS Center, Rutgers University, Piscataway, NJ Organizing Committee: Melvyn B. Nathanson, chair, Lehman College (CUNY) and IAS, nathansn@ias.edu George Andrews, Pennsylvania State University, andrews@math.psu.edu , David Chudnovsky, Polytechnic University of New York, david@gateway.imas.poly.edu Ronald L. Graham, ATT Labs and University of California at San Diego, rgraham@cs.ucsd.edu Jeffrey C. Lagarias, ATT Labs, jcl@research.att.com Victor S. Miller, Institute for Defense Analyses, victor@idaccr.org Andrew M. Odlyzko, ATT Labs, amo@research.att.com Carl Pomerance, Bell Labs, carlp@research.bell-labs.com Workshop Announcement Call for Participation Program Registration Form There is a $40 day registration fee, $5 day for non-DIMACS postdocs, to be collected on site, cash or check only. The fee is waived for graduate students and DIMACS long-term visitors and postdocs in residence at DIMACS. Fees for all members are covered through their institution's membership in DIMACS and therefore no member needs to pay the registration fee. Information on Accommodations Information on Travel Arrangements Parking Permit Parking permits will be available at the registration table on the day of the workshop. Important Reimbursement Information Attendees who have been offered support should keep two rules in mind. Reimbursement for air travel can only be made for travel on US Flag Carriers, REGARDLESS OF COST. (For example, travel on airlines such as United, Continental, USAir, and others that are United States based are allowable. Travel on airlines such as Lufthansa, SAS, Air Canada and other airlines based outside the US cannot be reimbursed by DIMACS.) The second rule to keep in mind is to get original receipts for all reimbursable expenses. Proceedings: Available through AMS (Volume 64 in the DIMACS Series): Ordering information, preface and table of contents . Other Workshops DIMACS Homepage Contacting the Center Document last modified on January 4, 2000.
School on Automorphic Forms on GL(n)
ICTP, Trieste, Italy; 31 July - 18 August 2000.
ICTP Mathematics Group: SMR 1233 Bulletin ICTP - The Abdus Salam International Centre for Theoretical Physics , Trieste, Italy School on Automorphic Forms on GL(n) Supported by the European Commission, Research DG, Human Potential Programme, High Level Scientific Conferences HPCF-CT-1999-00140 31 July - 18 August 2000 Miramare - Trieste, Italy The Abdus Salam International Centre for Theoretical Physics (ICTP), in conjunction with its mathematical theme of the year, Complex Algebraic Geometry and Algebraic Groups, is organizing a School on Automorphic Forms on GL(n) from 31 July to 18 August 2000. It will be directed by G. Harder (Universit228t Bonn Max-Planck-Institut f252r Mathematik, Germany) and M.S. Raghunathan (Tata Institute of Fundamental Research, Mumbai, India). PROGRAMME Automorphic Forms has been over the last century a central area in Mathematics, the Langlands programme being the principal preoccupation of many leading minds. In the recent past there have been many important developments in the area. The present School aims to introduce this deep and difficult area to research scholars and students with a relatively modest background. In a series of lectures over a period of 2 weeks, the following topics will be covered: - Abelian class field theory - Artin's L-functions and their meromorphy - Overview of Langlands programme - Summary of structure theory of representations of groups over local fields - Basic facts on automorphic forms (complete reducibility of spaces cusp forms, finite dimensionality of spaces of automorphic forms - Taniyama-Weil conjecture - Langlands programme for local fields - Analytic properties of L-functions of automorphic forms - Multiplicity 1 theorems In the third week of the School, there will be a research level Conference to which many leading experts have been invited. The speakers in the instructional part of the School will include the following: J. Cogdell (Oklahoma State University, Stillwater, U.S.A.) G. Harder (Universit228t Bonn Max-Planck-Institut f252r Mathematik, Germany) D. Prasad (Mehta Research Institute, Allahabad, India) M.S. Raghunathan (Tata Institute of Fundamental Research, Mumbai, India) T.N. Venkataramana (Tata Institute of Fundamental Research, Mumbai, India) T. Wedhorn (Universit228t zu K246ln, Germany) PARTICIPATION Mathematicians from all countries that are members of the UN, UNESCO or IAEA can attend the School. The main purpose of the Centre is to help research workers from developing countries through a programme of training activities within a framework of international cooperation. However, students and post-doctoral scientists from developed countries are also welcome to attend. As the School will be conducted in English, participants should have an adequate working knowledge of that language. Participants should preferably have completed some years of study and research after a first degree. There is no registration fee for participation in the School. As a rule, all expenses of the participants should be borne by the home institution. However, a limited number of financial grants are available for participants from developing countries. As scarcity of funds allows travel to be granted only in few exceptional cases, every effort should be made by candidates to secure support for their fares (or at least half of their fares) from their home country. Graduate and doctoral students should include with their application two letters of recommendation. EC GRANTS FOR YOUNG RESEARCHERS IN EUROPE A grant from the European Commission will make it possible to provide financial support (travel and or subsistence) for some young researchers in Europe who both qualify for the School and satisfy the Age and Residence Criteria. Age Criterion Young researchers are researchers up to an age limit of 35 years at the time of the event. Allowance will be made for compulsory military or civil service (actual time spent in military or civil service) and childcare (maximum 2 years per child for the actual time spent off work). Residence Criterion Young researchers who are nationals of a Member State of the European Union* or an Associated State**, and active inside a Member State or an Associated State at the time of the Event. _________________________ * Member States of the European Union Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxemburg, Netherlands, Portugal, Spain, Sweden, United Kingdom. ** Associated States Bulgaria, Cyprus, Czech Republic, Estonia, Hungary, Iceland, Israel, Latvia, Liechtenstein, Lithuania, Norway, Poland, Romania, Slovakia, Slovenia. The closing date for submitting requests for participation is 31 March 2000. The decision of the organizers will be communicated to all candidates as soon as possible thereafter. The "Request for Participation" ( text version , postScript version , pdf version ),(obtainable also via electronic mail: smr1233@ictp.trieste.it , using as Subject: get announcement) should be completed, signed and mailed to: School on Automorphic Forms on GL(n) (c o Ms. A. Bergamo) Strada Costiera 11 I-34014 Trieste Italy Tel.: +39 040 2240201 Fax: +39 040 2240490 Trieste, November 1999 Please report any problem on this page to zetto@ictp.trieste.it . BACK to ICTP Mathematics Group - 2000 Activities BACK to Mathematics Group Home Page
q-series with Applications to Combinatorics, Number Theory and Physics
University of Illinois at Urbana-Champaign, USA; 26--28 October 2000.
qseries conference q-series with Applications to Combinatorics, Number Theory and Physics. October 26-28, 2000 University of Illinois at Urbana-Champaign. Plenary Speakers Scott Ahlgren (Colgate University) George Andrews (Penn State University) Richard Askey (University of Wisconsin) Anne Schilling (MIT) Dennis Stanton (University of Minnesota) Special Note: Some of the plenary lectures will highlight open problems and future trends. Invited Speakers Krishnaswami Alladi (University of Florida) Douglas Bowman (University of Illinois) Youn-Seo Choi (Korea Institute for Advanced Study) Thomas Ernst (Uppsala University) Tina Garrett (University of Minnesota) Frank Garvan (University of Florida) Christian Krattenthaler (University of Vienna) Jeremy Lovejoy (University of Wisconsin) Steve Milne (Ohio State University) Katsuhisa Mimachi (Kyushu University) Morris Newman (University of California, Santa Barbara) Peter Paule (University of Linz) Sasha Polishchuk (Boston University) Sergei Suslov (Arizona State University) Ole Warnaar (Melbourne University) Sander Zwegers (University of Utrecht) Contributed Talks (September 15, 2000 Deadline for titles and abstracts) David Bradley (University of Maine, Orono) Matthew Boylan (University of Wisconsin) Guemlan Choi (University of Illinois) Shaun Cooper (University of Minnesota) Sylvie Corteel (Universite de Versailles) Larry Ericksen Yasushi Kajihara (Kobe University) Louis Kolitsch (University of Tennessee at Martin) Zhi Guo Liu (Xinxiang University) Richard McIntosh (University of Regina) David Penniston (Furman University) Axel Riese (University of Linz) Neville Robbins (San Francisco State University) Michael Schlosser (Ohio State University) Slobodan Trickovic (Nis University, Yuogslavia) Jan Felipe van Diejen (Universidad Chile) Ae Ja Yee (KAIST, Korea) Schedule of Events October 26, 2000 Conference Banquet (Illini Union) October 27, 2000 Concert by C. Krattenthaler (Levis Faculty Center) October 28, 2000 Party (Home of Bruce and Helen Berndt). Registration: Fill out the Registration form with checks made payable to the University of Illinois, and return them to: Bruce Berndt Department of Mathematics 1409 W. Green Street University of Illinois Urbana, Illinois 61801 To be placed an an e-mail list, send an e-mail to berndt@math.uiuc.edu Travel If you travel by air, we recommend that you book your flights into Champaign, Illinois. The Champaign Airport is relatively small, but it is conveniently located (a 15 minute drive to campus) and is served by four major airlines: American Airlines, Northwest Airlines, TWA and US Airways. The closest major airports are in Indianapolis (2 hours by car), Chicago (3 hours by car) and St. Louis (3 hours by car). If you decide to book your flight to one of these cities, we recommend that you rent a car at the airport and drive to Champaign, as public transportation between these cities and Champaign is not very convenient. Visa Information. Visa Types: The two main types of short term visas are B-1 and B-2. The B-1 visa is for business travel, while the B-2 visa is intended for tourist visits. Conference participants who require a visa and who expect to receive partial support for travel expenses must obtain a B-1 Business visa. Make sure that B-1 Business is indicated on your I-94 card. The University is not allowed to pay participants who have entered the US on a B-2 visa or a B-1 Tourist visa. Visa Waivers:Visas are not necessary for participants from countries covered by the visa waiver program (which include most European countries, Australia and Japan). Visitors from those countries will be issued a visa waiver when passing through US Customs and Immigration. The waiver will be one of two forms: WB or WT. Participants expecting to receive partial support for travel expenses must obtain a WB waiver. The University is not allowed to pay participants who have entered the US on a WT waiver. Venue and Hotel Reservations Click here for Venue and Hotel Information. Conference Proceedings: We will publish a proceedings of this conference in the American Mathematical Society Contemporary Mathematics series. Papers must be submitted by January 1, 2001. Funding: Due to generous support from the David and Lucile Packard Foundation, the National Science Foundation and the Number Theory Foundation, financial support is available to a limited number of partcipants with some preference given to graduate students and new PhD's. To apply for this support, send e-mail to ono@math.wisc.edu by September 1, 2000. Scientific Organizers Bruce Berndt and Ken Ono
Number Theory Day 2000
A special session of the 5th Pan African Congress of Mathematicians (PACOM'2000). University of Witswatersrand, South Africa; 21 January 2000.
NUMBER THEORY DAY 2000 AND PACOM2000 The John Knopfmacher Centre for Applicable Analysis and Number Theory NUMBER THEORY DAY 2000 AND PACOM2000 - SPECIAL SESSION IN NUMBER THEORY AND COMBINATORICS On behalf of the organising committee we are pleased to invite you to attend and present talks at these two events, which will be dedicated to John Knopfmacher , a South African number theorist of international renown who died tragically of a heart attack on 29 May 1999, during a stay as a visiting Professor in Austria. A description of his life and career can be found on his home page . The 5th Pan African Congress of Mathematicians PACOM'2000 , will take place at the Western Cape University of Cape Town, South Africa, from January 23rd to January 28th 2000. The Pan African Congress of Mathematicians (PACOM), is hosted by an African country every four years, as a major scientific event open to all mathematicians. This event also forms part of the worldwide Mathematics Year 2000 activities. For PACOM 2000 the theme of the congress is: Africa in the World Mathematical Year 2000: Assessment and promotion of mathematics education and research at the dawn of the 3rd millennium. Further information about the congress is available on the web site http: science.up.ac.za pacom. For addional information on the special session on NUMBER THEORY AND COMBINATORICS please contact one of the organisers below. In conjunction with this event a NUMBER THEORY DAY 2000 will be held at the University of Witswatersrand, Johannesburg, on Friday 21 January 2000. This event will be sponsored by The John Knopfmacher Centre for Applicable Analysis and Number Theory LIST OF POTENTIAL SPEAKERS Neville Robbins Jean-Paul Allouche Joachim von zur Gathen Daniel Panario Gert Almkvist Doron Lubinsky James Ridley Lutz Lucht Wolfgang Schwarz Pelegri Viader Christian Mauduit Arnold Knopfmacher Helmut Prodinger Peter J. Grabner Frederique Bassino Richard Brak Abdelmalek Azizi Oumar Mbodj Richard Warlimont NUMBER THEORY DAY 2000 - Program and Abstracts PACOM2000 - SPECIAL SESSION ABSTRACTS The latex file containing all speaker's abstracts is available for download from here . GENERAL INFORMATION Cape Town in summer is one of the most beautiful cities of the world with its coastal scenery, Table Mountain and famous beaches. The weakness of the South African currency againt the Euro and Dollar makes the cost of food and accomodation very cheap for overseas participants. The organisers of PACOM2000 have put together an impressive sightseeing program which is described on their web page. FINANCIAL ASSISTANCE AND DEADLINES Unfortunately we are unable to pay the cost of airfares for attending speakers, however the Centre for Applicable Analysis and Number Theory may be able to contribute some local cost to speakers at NUMBER THEORY DAY 2000. For organisational and subsidy purposes we would appreciate it if you could let us know before August 10 1999 if you are potentially interested to attend these events. The actual deadline for registration is 30th October 1999. Please feel free to pass this announcement on to others who might be interested in participating. Sincerely The Local Organising Committee (Number Theory Day 2000 and PACOM special session): Arnold Knopfmacher - arnoldk@cam.wits.ac.za Helmut Prodinger - helmut@cam.wits.ac.za Foreign Organiser (PACOM special session): Peter J. Grabner - grabner@weyl.math.tu-graz.ac.at
Kloosterman Centennial Celebration
Universiteit Leiden, the Netherlands; 7 April 2000.
Kloosterman Centennial Celebration Kloosterman Centennial Celebration Universiteit Leiden April 7, 2000 Hendrik Douwe Kloosterman was born on April 9, 1900. After studying in Leiden, Copenhagen, Oxford, Gttingen and Hamburg he held a professorship in mathematics at the Universiteit Leiden from 1930 until his death in 1968. Kloosterman made important contributions to mathematics. He is particularly well-known for the introduction and study of "Kloosterman sums". On Friday April 7, 2000 the Mathematical Institute and the Lorentz Center of the Universiteit Leiden are organizing a Kloosterman Centennial Celebration. An announcement in Dutch is available in Postscript. The program for the day is as follows 10:30 G. van Dijk Opening 10:30-11:30 T.A. Springer Kloosterman's work on representations of finite modular groups 12:00-13:00 D.R. Heath-Brown Arithmetic applications of Kloosterman sums 13:00-14:30 Lunch 14:30-15:30 P. Sarnak Kloosterman, quadratic forms and modular forms 16:00-16:30 N.G. de Bruijn Remembering Kloosterman Reception after the last lecture The lectures will take place at the The Lorentz Center , which is located across the street from the Mathematical Institute. In order to attend the lectures and join the complementary lunch please register with Hans van Bemmel by sending email to him at bemmel@lc.leidenuniv.nl or paper mail at Lorentz Center, P.O. Box 9506, 2300 RA Leiden. We will also organize a dinner, which will cost about NLG 80, and for which you can also register with Hans van Bemmel. We need to have the full list of lunch and dinner participants by March 30. The organizing committee consists of J. Murre murre@math.leidenuniv.nl H.W. Lenstra, Jr. R. Tijdeman Dr. B. de Smit desmit@math.leidenuniv.nl Last modified by desmit@math.leidenuniv.nl on Wednesday, 23-Feb-2000 17:34:27 CET.
International Workshop on Number Theory
In honor of Professor Chao Ko's 90-th Birthday. Sichuan University, Chengdu, China; 20--24 July 2000.
Ko's Conference Page International Workshop on Number Theory in honor of Professor Chao Ko's 90-th Birthday July 20-24, 2000 Sichuan University, Chengdu, P.R. China Topics: This conference will focus on arithmetic algebraic geometry, analytic number theory, arithmetic of function fields, L-functions, diophantine equations, and applications of number theory in cryptography. Sponsors: Chinese Ministry of Education Chinese National Science Foundation Sichuan University Scientific Committee: Yuan Wang (Chair) Keqing Feng (Co-Chair) Qi Sun (Co-Chair) Dingyi Pei Tao Zhan Zhaohua Jia Shouwu Zhang (USA) Daqing Wan (USA) Mingzhe Liao (Hong Kong) Jing Yu (Taiwan). Organizing Committee: Tiecheng Lu (Chair) Yingming Liu (Co-Chair) Anming Li (Co-Chair) Daoyi Xu (Secretary-General) Shijun Yan Ze Han Qifan Zhang Guohua Peng Format: In addition to some invited lectures, we anticipate a small number of contributed lectures. Abstracts of contributed papers should be received by April 30, 2000. Abstracts should be typed in LaTeX, not to exceed one page and sent by email to Prof. Guohua Peng (ghpeng@mail.sc.cninfo.net) or Prof. Qifan Zhang (sszibbh@mail.sc.cninfo.net). Information: For more information, please contact Prof. Guohua Peng or Prof. Qifan Zhang at the above email addresses, or the usual address: Department of Mathematics, Sichuan University, Chengdu 610064, China. Registration: The registration fee for the conference is US $100 including meals, refreshments, a banquet, final program and abstract. Accommodation and Tour: The Conference will be held at Sichuan University. It is planned to accommodate the participants in Ke Hua Yuan Hotel (~US$25), located in the adjacent west campus of Sichuan University. Tours to Jiu Zhai Gou Resort (RMB 1000--1500 = $120-180 for five days including travel, hotels and meals), and Emei Mountain and Leshan Giant Buddha (RMB450-750 = $60-90 for three days including travel, hotels and meals) will be arranged after the conference. Last modified December 25, 1999.
Instructional Conference on Fermat's Last Theorem
University of Illinois at Urbana-Champaign, USA; 6--18 August 2000.
Note: The deadline below passed but there are still a few open spaces. If you or your student is interested, please contact us as soon as possible! Instructional Conference on Fermat's Last Theorem August 6-18, 2000 University of Illinois at Urbana-Champaign Organizing Committee: Nigel Boston , UIUC Chris Skinner, IAS and Michigan From August 6-18, 2000, the Instructional Conference on Fermat's Last Theorem will be held as one of the featured events in a Special Year in Number Theory at the University of Illinois. It is intended to provide advanced graduate students with a detailed overview of the recent proof of Fermat's Last Theorem. Workshop participants will arrive Sunday, August 6 and leave at about lunchtime Friday, August 18. The meeting will consist of morning lectures by each of the organizers, followed by breaking into 4 groups of 6 students each to work on projects. These projects will fill some of the holes left in the lectures. Towards the end of the two weeks, students will present talks on their group work. There will be some social events (a reception at the start, an outing in the middle, and banquet at the end). Sponsors The conference is hosted by the Mathematics Department at the University of Illinois and is supported by the Number Theory Foundation and the National Science Foundation. Accommodations We have double occupancy rooms reserved at the Hendrick House for $15 or $17 per night per person (plus 11% tax). These are reserved for the nights of August 6-17 inclusively. They come with meal plans of $87 per week and excellent amenities. Travel Urbana-Champaign is at the meeting point of three Interstate freeways, I-57, I-72, and I-74. This will tell you about parking. Urbana-Champaign is also conveniently served by Champaign (Willard) airport . American Airlines, TWA, and Northwest Airlines fly into Champaign. Financial Support A large amount of funding is available to facilitate attendance by graduate students who do not have access to support through their own institution or their advisors. We expect to be able to pay people's expenses up to $800. Estimating local costs at $400 and travel costs at $400, this should cover everything. Registration Space limits this meeting to 20 out-of-town students plus 4 local students. (Other local students can attend the lectures but not the group sessions.) If you wish to attend this meeting, you must send by email to Nigel Boston your name, affiliation, and a statement of why you wish to attend the workshop (at most one page). Also, please indicate your gender and any preferences you might have as to room-sharing. Also, you must have your advisor send us a letter of recommendation to arrive by May 20. This letter should indicate what level of background you have had in algebraic number theory, commutative algebra, and algebraic geometry. We will tell you by May 27 as to whether your application has been successful. About the Organizers Nigel grew up in England, did his undergraduate work at Cambridge University, and got his Ph.D. with Barry Mazur from Harvard in 1987. His thesis work was in deformations of Galois representations. After a year in Paris and two in Berkeley, he went to the University of Illinois where he has been ever since, except for six months at the Newton Institute, during which time Andrew Wiles first announced a proof of Fermat's Last Theorem. He has written an expository article on the proof for the College Mathematics Journal and has taught a graduate course on it. His research is in algebraic number theory, group theory, and lately applications of arithmetical geometry to engineering. Chris grew up in Little Rock, Arkansas. He went off to college to the University of Michigan, from which he received a B.S. in Mathematics in 1993. In 1997 he received his Ph.D. from Princeton University where he was a student of Andrew Wiles. He was fortunate to be around Princeton during the exciting days surrounding the proof of Fermat's Last Theorem. Since 1997 he has been a member of the Institute for Advanced Study, and in the fall of 2000 he will join the faculty of the Department of Mathematics at the University of Michigan. These days his research focuses on the modularity of Galois representations and other arithmetic aspects of automorphic forms. For further information, contact: Nigel Boston , University of Illinois at Urbana-Champaign (217 333-2677) Chris Skinner , Institute for Advanced Studies (609 734-8145)
Illinois Graduate Number Theory Conference 2000
University of Illinois at Urbana-Champaign, USA; 25--26 March 2000.
2000 Illinois Graduate Number Theory Conference March 25 26, 2000 University of Illinois at Urbana-Champaign Organizing Committee: Michael Bennett, UIUC Mark Bauer, UIUC In March 2000, the 2000 Illinois Graduate Number Theory Conference will be held as one of the featured events in a Special Year in Number Theory at the University of Illinois. It will be comprised of contributed talks in any and all areas of Number Theory, by graduate students, be they early career or finishing PhDs. The aim of the conference is to provide a low-stress forum for students to meet other students with comparable interests, practice "job talks" or just gain valuable experience. There will be an opportunity for each participant to deliver a contributed talk of 20 minutes duration, should they choose to do so. The conference begins Saturday, March 25th at 9am and concludes in the afternoon on Sunday, March 26th. Sponsors The conference is hosted by the Mathematics Department at the University of Illinois and is supported by the Number Theory Foundation. Accommodations We have rooms reserved at the Sleep Inn for $50 per night. These are reserved under the department's name and are for the nights of March 24-26. If you have any further questions please contact me at mabennet@math.uiuc.edu . Travel Urbana-Champaign is at the meeting point of three Interstate freeways, I-57, I-72, and I-74. This will tell you about parking. Urbana-Champaign is also conveniently served by Champaign (Willard) airport . American Airlines, TWA, US Airways, and Northwest Airlines fly into Champaign. The hotel has courtesy vans. Please arrange to have them meet you. Financial Support A limited amount of funding is available to facilitate attendance by graduate students who do not have access to support through their own institution or their advisors. If you are interested in applying for such support, contact Mike Bennett ( mabennet@math.uiuc.edu ). Registration There will be no registration fee. We do ask, though, that those planning to attend the conference formally register using the registration form. A copy of the registration form may be obtained by contacting Mike Bennett ( mabennet@math.uiuc.edu ) or Mark Bauer ( m-bauer@math.uiuc.edu ). For further information, contact: Michael Bennett , University of Illinois at Urbana-Champaign (217 244-3367) Mark Bauer , University of Illinois at Urbana-Champaign (217 333-6328)
Conference in Honour of David Burgess' 65th Birthday
Nottingham, UK; 4--6 February 2000.
Burgess Meeting Conference in honour of David Burgess Nottingham, February 4-6, 2000 Organizers R. Heath-Brown, J. Cremona, I. Fesenko Invited speakers Peter Elliott, Colorado Etienne Fouvry, Orsay Heini Halberstam, Urbana Roger Heath-Brown, Oxford C. Hooley, Cardiff Martin Huxley, Cardiff Henryk Iwaniec, Rutgers Gerald Tenenbaum, Nancy A meeting in honour of Professor David Burgess's 65th burthday will be held in February 2000, at the Nottingham Royal Moat House Hotel, with support from the London Mathematical Society. programme (revised 11 January 2000) How to get here For registration information and further details, please email John Cremona: John.Cremona@nottingham.ac.uk. Page maintained by John Cremona
Pacific Northwest Number Theory Conference
University of Washington, Seattle, USA; 17 April 1999.
Third Annual Pacific Northwest Number Theory Conference THE THIRD ANNUAL PACIFIC NORTHWEST NUMBER THEORY CONFERENCE This will take place in Seattle, Washington on the campus of the University of Washington on April 17th, 1999. The conference is supported by the Milliman Fund and by the Number Theory Foundation. The organizers are Joe Buhler and Ralph Greenberg. INVITED SPEAKERS BILL CASSELMAN University of British Columbia PICTURING ARITHMETIC QUOTIENTS _________________________________ ADRIAN IOVITA University of Washington p-ADIC L-FUNCTIONS ATTACHED TO ELLIPTIC CURVES __________________________________ KARL RUBIN Stanford University RANKS OF ELLIPTIC CURVES IN FAMILIES OF QUADRATIC TWISTS __________________________________ JOHN TATE University of Texas CLASS NUMBER FORMULAS, CLASSICAL AND "REFINED" __________________________________ INFORMATION ABOUT THE SCHEDULE AND LOCATION OF TALKS CAN BE FOUND HERE . ACCOMMODATIONS NEAR THE CAMPUS UNIVERSITY MOTEL: 4731 12th Ave NE, Seattle, WA 98105 206-522-4724 Single $59.00, Double $75.00, Triple $81.00 UNIVERSITY INN: 4140 Roosevelt Way NE, Seattle, WA 98105 206-632-5055, 800-733-3855 Single $79.00, Double $89.00 http: www.universityinnseattle.com SILVER CLOUD INN: 5036 25th Ave NE, Seattle, WA 98105 206-526-5200, 800-205-6940 Single $79.00, Double $89.00 (PNWNTC Rate) http: www.scinns.com universi.htm TRAVELODGE: 4725 25th Ave NE, Seattle, WA 98105 206-525-4612, 800-578-7878 Single $69.00, Double $79.00 (PNWNTC Rate) COLLEGE INN: 4000 University Way NE, Seattle, WA 98105 206-633-4441 Single $54.00, Double $74.00 (PNWNTC Rate) These rooms are without private bath http: www.speakeasy.org collegeinn LINKS FOR OTHER LODGING POSSIBILITIES: http: www.seeseattle.org lodguide LODGHOME.HTM http: www.seeseattle.org lodguide hostels.htm http: www.seeseattle.org lodguide BBSea.htm For additional information: Please contact Ralph Greenberg 206-543-7648, greenber@math.washington.edu
Model Theory and Number Theory
Workshop. University of Illinois at Urbana-Champaign, USA; 13--14 November 1999.
Model Theory and Number Theory Conference Model Theory and Number Theory Conference November 13 14, 1999 University of Illinois at Urbana-Champaign SCHEDULE OF TALKS All lectures will take place in Room 245 Altgeld Hall, 1409 West Green St., Urbana. Saturday, November 13, 1999 10:00 am Thomas Scanlon (Berkeley), Manin-Mumford for additive groups 11:00 am Alexandru Buium (New Mexico and Illinois), An arithmetic analogue of the Euler-Lagrange formalism 2:00 pm Lou van den Dries (Illinois), On a question of Serre in connection with Hilbert's irreducibility theorem 3:00 pm Daniel Bertrand (Paris VI), Arithmetic theory of differential equations 4:00 pm Zoe Chatzidakis (Paris VII), Questions and progress on groups definable in difference fields Sunday, November 14, 1999 10:00 am Minhyong Kim (Arizona), Diophantine height inequalities 11:00 am Anand Pillay (Illinois), Mordell-Lang for complex tori TRAVEL A block of rooms has been reserved at the Quality Hotel, 302 E. John St., Champaign. The hotel is a five minutes walk from Altgeld Hall. Please make reseravations by calling the hotel at 1-800-322-8282 or 217-384-2100. (Also please let A. Pillay know when you have made the reservation.) If you are coming by plane or Amtrak and staying at the Quality Hotel, you can use the complimentary shuttle service provided by the hotel. Call the hotel (1-800-322-8282 or 384-2100) on one of the public phones to request the hotel shuttle. In addition to hotel courtesy vans, there is a door-to-door shuttle service between the airport and Champaign-Urbana; the cost is $9 each way. DRIVING DIRECTIONS TO THE QUALITY HOTEL AND TO ALTGELD HALL From I-74, take the Lincoln Avenue exit in Urbana, go south on Lincoln for about 1 1 2 miles to the light on Green Street, turn right (west) onto Green Street, go about 1 2 mile west on Green Street, crossing Goodwin, Wright, 6th, 5th, and 4th Streets, turn left (south) on 3rd Street. The Quality Hotel is a high rise building half a block to your left, at the intersection of John St. and 4th St. If you are staying at the hotel, you can park your car in the hotel`s parking garage. Altgeld Hall is the historic building with a bell tower on the southeast corner of the intersection of Green and Wright Streets. Parking is available one block from Altgeld Hall, in the University parking garage at the intersection of John St. and 6th St. To reach the parking garage, follow the directions above, but turn left (south) two blocks earlier, on 5th St., then turn left (east) again onto John St. The garage is to your right. From I-72 and I-57, follow the directions to I-74 east, and then continue as above. Further directions, and maps of the UIUC campus and the Champaign-Urbana area, can be found at http: www.uiuc.edu under "Campus Maps". FINANCIAL SUPPORT We will cover hotel expenses for graduate students as well as contributing to other expenses if possible. MORE INFORMATION For more information, contact A. Pillay (pillay@math.uiuc.edu, phone 217-355-3869) or A. Buium (buium@math.unm.edu).
Illinois Number Theory Conference
University of Illinois at Urbana-Champaign, USA; 17--18 September 1999.
1999 Illinois Number Theory Conference Illinois Number Theory Conference September 17-18, 1999 University of Illinois at Urbana-Champaign Information for participants (updated 9 7 1999) Schedule of talks (updated 9 16 1999) Conference Program The 1999 Illinois Number Theory Conference will mark the beginning of a Special Year in Number Theory at the University of Illinois. It will feature hour talks by K.Alladi (University of Florida), P. Borwein (Simon Fraser University), A. Pollington (Brigham Young University), and K.S. Williams (Carleton University), and there will be opportunities for contributed talks of 20 minutes duration. The Illinois Number Theory Conferences are annual two day meetings, usually held in the Spring at the University of Illinois or at a neighboring university. The main focus of these conferences is on the areas of elementary, combinatorial, analytic, computational, and probabilistic number theory. The algebraic side of number theory is covered by a similar series of meetings, the Midwest Algebraic Number Theory Days. The conference begins Friday, September 17, 1999, at 9:00 a.m., and will end Saturday evening. Sponsors The conference is hosted by the Mathematics Department at the University of Illinois and is supported by the Number Theory Foundation and the National Science Foundation. Contributed Talks A limited number of slots is available for 20 minute contributed talks. The deadline for requesting a contributed talk is August 15, 1999. If you are interested in giving a contributed talk, please use the online registration form . Accommodations We strongly recommend that you stay at the Quality Inn - University Center (formerly the University Inn). A block of rooms has been reserved at this hotel for the nights of September 16 - 18, 1999, at the rate of $50 per night plus tax. The hotel is centrally located in the Champaign campus area and will be the site of all talks on Friday, and of the conference banquet scheduled for Friday evening. (On Saturday, talks will be given in the UIUC mathematics department, located four blocks from the hotel.) Hotel guests can park for free in the hotel parking garage. Reservations should be made directly with the hotel, by calling 800-322-8282 or 217-384-2100 and identifying yourself as a participant of the Illinois Number Theory Conference. The reservation deadline is August 15, 1999; after that date, the rooms will be released and may no longer be available. Travel The Champaign airport is served by American Airlines, TWA, US Airways, and Northwest Airlines. The Quality Inn provides free shuttle service to and from the airport. Financial Support A limited amount of funding is available to facilitate attendance by recent PhD's and advanced graduate students who do not have access to support through their own institution or their advisors. Any support will likely be limited to reimbursement of local expenses, and other sources of funding, such as research grants or support from the home institution, should be exhausted first. If you are interested in applying for such support, contact Harold Diamond (diamond@math.uiuc.edu); for graduate students, the thesis advisor should submit a supporting letter. Registration In keeping with a long-standing tradition, we do not charge a registration fee. We do ask, though, that those planning to attend the conference formally register using the online registration form. You can either download (save) the form and send it by email, or print out and send the form by regular mail. All registered participants will receive, via email, a schedule of talks about two weeks before the conference. Additional information Updated information will be posted on this site (http: www.math.uiuc.edu nt2000 illinois), as it becomes available. If you have questions, feel free to contact the organizers, Harold Diamond (diamond@math.uiuc.edu) or A.J. Hildebrand (ajh@math.uiuc.edu). Last modified Sep-1-1999 ajh@uiuc.edu
Millennial Conference on Number Theory
University of Illinois at Urbana-Champaign, USA; 21--26 May 2000. Abstracts, photos.
Millennial Conference on Number Theory - Final Announcement Millennial Conference on Number Theory May 21 - 26, 2000 University of Illinois at Urbana-Champaign Conference Wrap-Up Group Photo (jpeg file [1,270k]) List of Participants (ps file [87k]) Titles of Talks (ps file [99k]) Abstracts (ps file [324k]) Abstracts in html format (from AMCA abstract server) Conference Program Second announcement First announcement Conference statistics A total of 276 participants have registered for and attended the conference. An additional 11 number theorists registered for the conference, but could not attend in person. The participants represented 30 countries, ranging from the U.S. and Canada to European countries and to far-away places such as Fiji, Japan, Taiwan, China, and Australia. The conference featured 157 talks , of which 19 were one-hour plenary talks, 73 half-hour invited talks given in 4 parallel sessions, and 65 contributed talks given in 5 parallel sessions. In addition to these scientific talks, the conference included three 40 minute talks of historical and reminiscing flavor, and several after dinner speeches honoring Professor Emeritus Paul Bateman on his 80th birthday. Conference Proceedings The Conference Proceedings will be published by A K Peters in a projected set of two volumes totaling approximately 1000 pages. In addition to these traditional style proceedings, A K Peters will publish an economically priced paperback volume containing selected survey lectures given at the conference. The Proceedings are scheduled to appear in mid 2001. General guidelines: All speakers are invited to submit a paper for these proceedings. Papers should normally be based on (or at least closely connected with) the talk given at the conference. In addition to original research papers, we welcome well-written survey papers. Because of restrictions on the size of the volumes, shorter papers are preferred, and we may not be able to consider excessively long papers. (Plenary speakers do not fall under this restriction.) Refereeing: Research papers will be refereed using the standards of journals such as the Journal of Number Theory, Acta Arithmetica, the Journal de Theorie des Nombres de Bordeaux, and The Ramanujan Journal. We will make every effort to ensure timely refereeing, and we thank in advance the referees (many of whom will be selected from among the conference participants) for their work. Technical preparation of papers: If possible, papers should be prepared in LaTeX, with a font size of 10 points, and textheight and textwidth set to 42pc and 27pc, respectively. To achieve these dimensions, proceed as follows: For papers in LaTeX: use 10 point font size, and specify the following settings in the preamble (before \begin{document}): \textheight42pc \textwidth27pc For papers in AmSTeX amsppt, use 10 point font size (default), and specify the following at the beginning of the paper, but after \documentstyle{amsppt}. \pageheight{42pc} \pagewidth{27pc} For papers in Plain TeX: use 10 point font size (default) and specify the following at the beginning of the manuscript: \vsize42pc \hsize27pc Submission procedure: Papers can be submitted either electronically or as a hard copy. For hard copy submission, send two copies of the paper to the member of the Organizing Committee (B.C. Berndt, N. Boston, H.G. Diamond, A.J. Hildebrand, and W. Philipp, all at the Univ. of Illinois, Dept. of Mathematics, Urbana, IL 61801) most appropriate for the paper. For electronic submission, send your tex file(s) to millennial-submit@math.uiuc.edu, along with a brief email cover letter. Papers received electronically will be processed and passed on to an appropriate editor. Please do not send submit both an electronic file and a hard copy. The deadline for submission of manuscripts is September 30, 2000. Acknowledgements The organizers gratefully acknowledge the following organizations for providing financial support to the conference: The Number Theory Foundation The National Science Foundation The National Security Agency The University of Illinois The Institute for Mathematics and Applications We are particularly grateful to the University of Illinois Mathematics Department for providing financial, logistical, and staff support for the conference, and for offering its facilities in Altgeld Hall for use the conference. The conference would not have been possible without the help provided by our own graduate students and by mathematics staff members. We are especially grateful to Betsy Gillies, conference coordinator of the mathematics department, who worked tirelessly behind the scenes to ensure that the conference would run smoothly. Contact addresses The Organizing Committee for the Conference consists of B.C. Berndt, N. Boston, H. Diamond, A.J. Hildebrand, from the University of Illinois Mathematics Department, and W. Philipp of the Statistics Department of the University of Illinois. For general questions or comments regarding the conference, please use the following contact addresses: Conference email address: millennial@math.uiuc.edu Conference web page: http: www.math.uiuc.edu nt2000 millennial. Mailing address: Millennial Conference Department of Mathematics University of Illinois 1409 West Green St. Urbana, IL 61801 USA Last modified Wed May 31 14:33:22 2000 ajh@uiuc.edu
Arithmetic Geometry
St. Petersburg, Russia; 20--26 June 2000. Photographs.
Arithmetic Geometry Conference Arithmetic Geometry St. Petersburg, Russia, June 20-26, 2000 Steklov Institute of Mathematics at St.Petersburg Euler International Mathematical Institute St.Petersburg State University Organisers: John Coates (Cambridge University) Sergei Vostokov (St. Petersburg University) Preliminary List of Participants: D. Benois (Russia France) M. Bondarko (Russia) I. Fesenko (UK) R. Greenberg (USA) U. Jannsen (Germany) M. Kurihara (Japan) S. Lichtenbaum (USA) F. Lorenz (Germany) Nguen Quang Do (France) J. Saito (Japan) N. Schappacher (France) A. Suslin (Russia) S. Vostokov (Russia) E. Urban (France) Yu. Zarkhin (USA) I. Zhukov (Russia) Photo album Preliminary Program Application Form Hotel information Useful Information Conference place Further Information: sergei@vostokov.usr.pu.ru Back to the EIMI home-page Back to the Steklov Institute of Mathematics at St.Petersburg
Thorie des Nombres, Bruit des Frquences et Tlcommunications
Institut Henri Poincar, Paris, France; 3-4 December 1999. English French. Abstracts.
telecom.html Institut de Mathmatiques de Jussieu UMR 7586 du CNRS Thorie des nombres, bruit des frquences et tlcommunications Institut Henri Poincar , Amphi Hermite Vendredi 3 et Samedi 4 Dcembre 1999 Les communications digitales modernes (tlphone sans fil, vido...) utilisent la modulation, le codage et le traitement de l'information sous des formes de plus en plus sophistiques, et qui empruntent largement la thorie des nombres. De plus, comme le transport de l'information module s'effectue sur des porteuses haute frquence, l'utilisation efficace de la bande passante dpend pour beaucoup des proprits des oscillateurs lectroniques et de leur synchronisation, ce qui est un problme d'approximation diophantienne. Plus prcisment on a observ que la comprhension du bruit des frquences fait appel aux proprits de la fonction zta de Riemann proximit de la droite critique. Cette rencontre, subventionne par le CNRS , a pour but d'informer sur les liens obtenus l'interface entre les problmes diophantiens, la physique quantique et la mtrologie des frquences. PROGRAMME: Vendredi 3 Dcembre 9h00-9h50 Michel Planat , Bruit des frquences sur un rcepteur de communication et fonction zta de Riemann 10h00-10h50 Francesco Amoroso, Distribution de la suite de Farey, Hypothse de Riemann et hauteur normalise de certains courbes 11h30-12h20 Jacky Cresson, Fractions continues et oscillateurs 14h30-15h20 Serge Perrine, Mathmatiques et Tlcommunications 15h30-16h20 Paula Cohen, Gomtrie non commutative et la fonction zta de Riemann et de Dedekind 17h00-17h50 Pierre Cartier, Fonction zta de Riemann, fonction zta de Selberg et dessins d'enfants 18h30 - Buffet l'Institut Henri Poincar Samedi 4 Dcembre 9h00-9h50 R. Balasubramanian, A few aspects of Riemann Hypothesis 10h00-10h50 Bernard Julia, Thorie des nombres et physique: multiplications ou additions? rigidit ou chaos? 11h30-12h20 Nina Snaith, Every moment brings a treasure: the Riemann zeta function and random matrix theory 14h30-15h20 Patrick Flandrin, Ondelettes et bruits en 1 f 15h30-16h20 Enrico Rubiola, Phase noise metrology 17h00-17h50 Jean-Michel Courty, Mesures quantiques non idales Si vous dsirez des renseignement, envoyez un message planat@jsbach.univ-fcomte.fr ou miw@math.jussieu.fr Vous pouvez tlcharger une version postscript: de l'annonce du programme des rsums des rfrences pour l'expos de Francesco Amoroso Vous pouvez aussi tlcharger des fichiers postscript ou zip contenant les textes de P. Cohen , J. Cresson , B. Julia , S. Perrine , M.Plana t, E. Rubiola , N. Snaith Institut de Mathmatiques de Jussieu UMR 7586 du CNRS Thorie des nombres, bruit des frquences et tlcommunications Institut Henri Poincar Vendredi 3 et Samedi 4 Dcembre 1999 RESUMS DES EXPOSS Francesco AMOROSO Distribution de la suite de Farey, Hypothse de Riemann et hauteur normalise de certains courbes On sait, depuis un article de Niederreiter, que la suite de Farey est uniformment distribue dans [0,1]. On sait aussi, depuis deux travaux clbres de Franel et Landau, que des bornes fines de la discrpance (qui mesure la qualit de la distribution) de cette suite sont lies l'hypothse de Riemann. Dans cet expos nous ferons le point sur ces rsultats. Nous prsenterons les travaux classiques cits et d'autres travaux (peut-tre moins connus) de Mikols, Codec, Perelli, Kanemitsu et Yoshimoto. Nous discuterons aussi de liens entre l'hypothse de Riemann et la hauteur normalise (au sens de Zhang et Philippon - David) de certains courbes dans G_m^2.. RFRENCES R. BALASUBRAMANIAN A few aspects of Riemann Hypothesis In this lecture we shall trace the number theoretic approaches to prove Riemann Hypothesis. This includes Lindelff Hypothesis, density results, the number of zeros on the line sigma=1 2 (Hardy-Selberg), mean value results, etc. We shall also discuss the order of zeta function on 1 2-line (omega results) (unconditionally and under Riemann Hypothesis). We shall briefly touch upon Montgomery's pari correlation conjecture (which goes beyond Riemann Hypothesis). Pierre CARTIER Fonction zta de Riemann, fonction zta de Selberg et dessins d'enfants A ct de la fonction de Riemann , Selberg a introduit une fonction dont on sait localiser les zros (partie relle 1 2) et qui lui ressemble beaucoup . Des expriences numriques menes par moi-mme , puis reprises grande chelle par Hejhal , ont permis de calculer de nombreux zros de cette fonction , interprts comme des valeurs propres. Je voudrais esquisser comment la gomtrie des lignes de niveau des fonctions propres associes pourrait s'interprter l'aide du thorme de Biely ("dessins d'enfant"). Paula COHEN Gomtrie non commutative et la fonction zta de Riemann et de Dedekind Nous reprenons l'tude d'un certain systme dynamique tudi par Bost et Connes et motiv par des travaux de B. Julia. Il s'agit d'un systme dynamique fonction de partition la fonction zta de Riemann et brisure spontane de symtrie au ple de cette fonction. L'approche rcente de Connes l'hypothse de Riemann y est relie. Une gnralisation de l'oratrice s'applique la fonction zta de Dedekind. Jean-Michel COURTY Mesures quantiques non idales Les amplificateurs sont des lments essentiels dans les mesures de haute prcision. Leur rle est d'amplifier le signal un niveau dtectable et aussi trs souvent de maintenir par rtroaction l'appareil de mesure son point de fonctionnement optimal. Une analyse raliste du processus de mesure ne peut donc ignorer la prsence de systmes actifs. Il est aussi ncessaire d'y associer une description prcise des phnomnes fondamentaux ainsi que des contraintes exprimentales. Ceci pose des questions fondamentales pour le problme de la mesure quantique. Quels sont les rles respectifs des fluctuations thermodynamiques et des fluctuations quantiques? Comment tenir compte des lments actifs dans une mesure quantique? Comment les contraintes exprimentales interagissent-elles avec les limites fondamentales de sensibilit? Je prsenterai cette problmatique et je l'illustrerai en discutant le cas d'un appareil rel, un acclromtre friction froide dvelopp pour des applications de physique fondamentale dans l'espace. Jacky CRESSON Fractions continues et oscillateurs En partant des expriences sur les oscillateurs de Michel Planat on construit un espace de nombres, rendant compte du spectre des frquences exprimental. Cet ensemble de nombres est construit sous une hypothse fondamentale: il existe une rsolution finie. La structure de cet ensemble est rendu claire via l'utilisation des fractions continues. Patrick FLANDRIN Ondelettes et bruits en 1 f L'analyse et la modlisation de bruits en 1 f posent des problmes lis leurs caractristiques de non-stationnarit, de longue dpendance ou de (multi-)fractalit. On montrera comment la transformation en ondelettes offre, par sa structure multirsolution, un langage naturel et un cadre unifi pour l'tude de tels processus. Divers modles (gaussiens, stables, d'auto-similarit tendue, de cascades) seront considrs dans le cadre du formalisme ondelettes, en lien avec des applications en turbulence dveloppe et en tltrafic informatique. Serge PERRINE Mathmatiques et Tlcommunications L'expos fera le point sur les domaines d'intrt commun entre Mathmatiques et Tlcommunications. Aprs une identification du domaine des Tlcommunications, et quelques rappels sur les liens historiques entre les deux domaines, on tentera une revue sur les domaines actuels d'intrt commun. Une des difficults de la prsentation est que les Tlcommunications font partie du domaine plus vaste du traitement de l'information, lui mme partie de domaines encore plus vastes des sciences de l'ingnieur. On fera donc quelques choix, guids par l'actualit du domaine. On voquera ce qui est relatif la modlisation, notamment autour d'Internet. On abordera les problmes de modlisation du trafic, ce qui est relatif la gestion de rseaux de routeurs, et bien entendu les problmes de codage de l'information. L'objet de l'expos est de montrer comment diffrents problmes techniques actuels peuvent dboucher sur de nouveaux problmes mathmatiques intressants. Il est intressant galement, en sens inverse, de montrer comment diffrents chapitres de mathmatiques considrs autrefois comme sans application possible peuvent aujourd'hui servir une meilleure comprhension de certains aspects des Tlcommunications. On mettra l'accent sur ce qui est relatif la gomtrie hyperbolique, aux formes modulaires, et l'arithmtique. On tentera, pour conclure, une revue des volutions l'oeuvre au niveau national et international dans le domaine des Tlcommunications, ainsi qu'une vocation des politiques repres la croise des deux grands domaines voqus ici. Michel PLANAT Bruit des frquences sur un rcepteur de communication et fonction zta de Riemann Dans un dispositif de communications, l'information est module sur un oscillateur (la porteuse) et compare un oscillateur local (de reference) au travers d'un mlangeur non linaire, ce qui permet de ramener le traitement de l'information en bande de base (au voisinage du continu). Ce principe n avec la radio revit actuellement avec les communications mobiles. Rcemment nous avons constat exprimentalement que le spectre des raies issues du mlange possde la dynamique des approximations diophantiennes. Les frquences du battement s'interprtent comme les fractions continues du rapport des frquences des oscillateurs d'entre. Les amplitudes du battement correspondent l'cart de la position des rationnels par rapport aux espacements uniformes. La phase de la fonction zta de Riemann sur (ou au voisinage) de la droite critique est la cl des fluctuations de phase du battement. On passera en revue les rsultats acquis l'interface entre les manips et la thorie des nombres premiers, et comment ils permettent d'envisager de nouvelles voies pour la modulation et le codage de l'information. Enrico RUBIOLA Phase noise metrology Phase noise, usually described in terms of the power spectrum density S_phi(f) of the phase fluctuation phi(t), is a relevant concern for high speed telecommunications, for research purposes and for space applications. The interferometric method seems to be the best choice for the measurement of S_phi in critical applications. In fact this method, compared to other ones, shows higher sensitivity, due to the low white and flicker instrument noise, a wider power range, and an improved immunity to low frequency magnetic fields. A sensitivity of the order of -180 dBrad^2 Hz (white) and -150 dBrad^2 Hz (flicker at 1 Hz) is not difficult to obtain, both in the HF-VHF and microwave regions. As the interferometric method allows to measure the instant phase in real time, it can be exploited to dynamically correct the phase noise of amplifiers and oscillators. If the real time measure is not needed -- as in the characterization of electronic components -- correlation and averaging techniques can be used to further improve the sensitivity. Correlating and averaging the output of two equal interferometers a noise compensation mechanism takes place; thus, the instrument noise floor S_phi_floor can be lower than the thermal energy kT referred to the carrier power Pc. Finally, an improved scheme makes use of a single amplifier that drives two detectors in quadrature with one another. Properly choosing the detection geometry, the phase noise measurement is still possible but the amplifier noise is rejected due to the quadrature condition. This is a joint work with Vincent Giordano Talk will be given in french. Nina SNAITH Every moment brings a treasure: the Riemann zeta function and random matrix theory The eigenvalues of large random unitary matrices have been conjectured to display the same statistics as the zeros of the Riemann zeta function high on the critical line. In our recent work we have been determining the extent to which investigations of random matrices can aid in the study of the moments of the zeta function averaged along the critical line, since mean values of the characteristic polynomials of these matrices offer a route for understanding the Riemann moments. Mise jour: 15 Janvier 2000 URL : http: www.math.jussieu.fr ~miw telecom.html
Relations with Arithmetic and Algebraic Geometry
Workshop on Hilbert's 10th problem. University of Gent, Belgium; 2--5 November 1999. Abstracts.
Hilbert 10 Workshop Hilbert's 10th problem, Relations with Arithmetic and Algebraic Geometry University of Gent, November 2-5 Het Pand Organisers: G. Cornelissen, J. Denef, A. Herremans, K. Hoornaert, L.Lipshitz, T. Pheidas, J. Van Geel, K. Zahidi Scientific committee: J. Denef, L.Lipshitz, T. Pheidas, J. Van Geel The organisation of this workshop is supported by the FWO and the FWO Research network WO.011.96N The main theme of the meeting The lectures Speakers and titles (abstracts) The Proceedings Preprints The Participants The main theme of the meeting was the relation between decidability problems, arithmetic and algebraic geometry. There were series of lectures with an instructional character with the following topics: Back to contents Work on Hilbert's 10th problem, for various rings and fields, over the past decades. Some model theoretic aspects and related decidability problems. Decidability for certain generic diophantine problems and for fragments of arithmetic. The algebraic geometric structure of Diophantine families. Mazur's conjectures on the topology of rational points. Computational aspects. Work of Rojas on (un)computability of bounds for integral points on curves and Diophantine sentences in four variables. Complexity of diophantine geometry. Back to contents 10. Entscheidung der Losbarkeit einer diophantischen Gleichung. Eine diophantische Gleichung mit irgendwelchen Unbekannten und mit ganzen rationalen Zahlkoefficienten sei vorgelegt: man soll ein Verfahren angeben, nach welchen sich mittels einer endlichen Anzahl von Operationen entscheiden lsst, ob die Gleichung in ganzen rationalen Zahlen losbar ist. Hilbert in 1900 Program for: Tuesday November 2 - Wednesday November 3 - Thursday November 4 - Friday November 5 List of speakers and titles ( Back to contents ) J.-L. Colliot-Thelene: Hasse principle and weak approximation for rational points of algebraic varieties : a survey (abstracts dvi file , ps file ) Double fibres and double covers: paucity of rational points. (abstracts dvi file , ps file ) L. Darniere: (Local-global principles), Decidability and nonsingular Hasse principle for rings. (abstract dvi file , ps file ) J. Denef: Hilbert's 10th problem for global fields in positive characteristic - Pheidas' proof Y. Ershov: (Local-global principles), Nice local-global fields M. Jarden: (Local-global principles), PSC Galois extensions of Hilbertian fields. (abstract dvi file , ps file ) L. Lipshitz: Analogues of Hilbert's 10th problem for algebraic domains - a survey. (abstract dvi file , ps file ) Y. Matjasevich: Hilbert's tenth problem: what was done and and was is to be done. Linear recurrent sequnces and Hilbert's Tenth Problem (abstract dvi file , ps file ) B. Moroz: On solubility of Diophantine equations (a survey of some results from analytic number theory). (abstract dvi file , ps file ) L. Morret-Bailly: (Local-global principles), Arithmetic and geometric applications of local-global principles. (abstract dvi file , ps file ) T. Pheidas: Hilbert's 10th problem for ${\bf R}(t)$ - Denef's proof. (abstract dvi file , ps file ) F. Point: Decidable extensions of Presburger arithmetic. (abstract dvi file , ps file ) B. Poonen: Sums of values of a rational function. A. Prestel: A uniform approach to Local-Global Principles (abstract dvi file , ps file ) M. Prunescu: A model-theoretic approach to diophantine definability.(abstract dvi file , ps file ) P. Ribenboim: The hypothesis H and the ABC conjecture. M. Rojas: Complexity of diophantine geometry On (un)computability of bounds for integral points on curves and Diophantine sentences in four variables. (abstract 1 dvi file , ps file ), (abstract 2 dvi file , ps file ),(abstract 3 dvi file , ps file ) A. Shlapentock: Hilbert's 10th problem for rings of algebraic numbers. Defining integrality at infinite sets of primes of high density Y. Tschinkel: Density of rational and integral points on algebraic varieties (abstract dvi file , ps file ) C. Videla: Undecidability of some infinite algebraic extensions of the rationals. M. Vserminov: Linear recurrent sequnces and Hilbert's Tenth Problem K. Zahidi: Existential undecidability for algebraic function fields. Back to contents Proceedings ( Back to contents ) We have a provisional acceptance of the AMS to publish the proceedings as a volume of Contemporary Mathematics. The following papers will appear in these proceedings. Hilbert's tenth problem: what was done and and was is to be done. Y. MATIJASEVICH Undecidability of existential theories of rings and fields: A survey T.PHEIDAS, K.ZAHIDI Hilbert's Tenth Problem over Number Fields, a Survey, A. SHLAPENTOKH Defining constant polynomials M. PRUNESCU Decidability and Local-Global Principles, L. DARNIERE Applications of Local-Global principles to Arithmetic and Geometry, L. MORET-BAILLY Regularly $T$-closed fields J.SCHMID Skolem density Problems over Large Galois Extensions of Global Fields, M. JARDEN, A. RAZON, W-D. GEYER An effort to prove that the existential theory of Q is undecidable, T.PHEIDAS Topology of Diophantine Sets: Remarks on Mazur's Conjectures, G.CORNELISSEN, K.ZAHIDI Diagonal quadratic forms and Hilbert's Tenth Problem P.VOJTA Low Dimensional Varieties and the Frontier of Tractability. M.ROJAS Some model theory of compact complex spaces, A. PILLAY Double coset decompositions for algebraic groups over K[t], K.H. KIM, F.W. ROUSH Zero Estimates for Polynomials in 3 and 4 Variables using Orbtis and Stabilisers, C.D. BENNETT, L.K. ELDERBROCK, A.M.W.GLASS Back to contents Participants: Belair, Bes, Boffa, Chatzidakis, Cherlin, Colliot-Thlne, Coppens, Cornelissen, Cluckers, Darniere, Davis, Delon, Denef, Donnely, Duret, Ersov, Gardeyn, Herremans, Hoornaert, Jarden, Lipshitz, Loeser, Matijasevich, Michaux, Moosa, Moret-Bailly, Moroz, Pheidas, Pierce, Pillay, Point, Poonen, Prestel, Prunescu, Razon, Ribenboim, Rojas, Segers, Shlapentokh, Sundaram, Tschinkel, Van Geel, Van Lierde, Veys, Vidaux, Videla, Vsemirnov, Zahidi. Back to contents The lectures were held in Het Pand a historical building in the old center of Gent which is used by the university for seminars and conferences. hilbrt10@cage.rug.ac.be Jan Van Geel or Karim Zahidi, University of Gent, Department of Pure Mathematics, Galglaan 2, B-9000 Gent, Belgium. Fax. 32 - (0) 9 - 264 49 93 Although we invite all people that are interested in the topics to apply, the number of participants will be limited in order to maintain the character of the meeting.
Coding theory, Cryptography, and Number Theory
USNA, Annapolis, MD, USA; 25--26 October 1998.
Conference on Coding theory, Cryptology, and Number Theory USNA Mathematics Department Coding theory, Cryptology, and Number Theory Conference Time: October 25 and 26, 1998 Place: USNA Math Dept, Chauvenet Hall, (most talks in C116, Peter Hilton's talk in C216) Coding theory and cryptology number theory will be on Sunday the 25th, with more cryptology number theory on Monday the 26th. Prof Hilton will speak Monday night the 26th. This conference is generously funded by the NSA. No registration fee for attending the conference but if you plan to attend, please email David Joyner at wdj@nadn.navy.mil or call at (410)293-6738. Main Speakers: Professor Peter Hilton SUNY, Binghamton and Univ. of Central Florida Time: 7-8pm, Monday Oct 26 Title: Breaking high grade German ciphers in WWII; working with Alan Turing Abstract: During World War II a team of mathematicians, and young would-be mathematicians, worked round the clock to break the highest grade German military and diplomatic codes. They were astonishingly successful, and as a result provided the allied war machine with an unprecedentedly complete picture of the enemy plans and dispositions. I was fortunate to be chosen to be a member of that team. In this talk I describe our work and the atmosphere in which it was conducted. I will further give a description of the special contribution of the famous logician Alan Turing, whom I knew well for the last 10 years of his tragically short life. Professor Carl Pomerance Univ Georgia Time: 1:00-1:50 pm, Sunday Oct 25 Title: Probability and Factoring Abstract: Some important cryptographic systems base their security on our supposed inability to factor large numbers. It thus becomes important to see just how hard this problem is. Some of the best factoring methods we have are modeled on some attractive results in probability theory. For example, the birthday paradox from elementary probability theory (which discusses how soon there will be a repeat when random integers are chosen from the interval [1,x] ) is the model for the ``rho'' factoring method of John Pollard. Consider a similar probabilistic problem: how soon will a subsequence have product a square when we choose integers randomly from [1,x] ? If we choose the same integer twice, as in the birthday problem, then we have the subsequence. But there are other ways to get a product to be a square other than just multiplying a number by itself. We shall show that the answer is quite different for this new probabilistic problem than for the birthday problem; and the factoring algorithms it leads to (the quadratic sieve and the number field sieve, among others) are much faster than the rho method. Dr. Neil J. A. Sloane ATT Shannon Labs Time: 5:00-5:50 pm, Sunday Oct 25 Title: Codes and Sphere Packings Abstract: An overview of the connections between coding theory and the problem of packing spheres in n-dimensional space. There have been exciting developments in the sphere packing problem this summer. Other speakers On Sunday (in C116 or C117): Bill Wardlaw (USNA, "The RSA Public Key Cipher Algorithm "), 2:00-2:35 pm, Oct 25, Samuel J. Lomonaco, Jr. , (UMBC, "Quantum Cryptographic Protocols or How Alice and Bob Outwit Eve") 2:45-3:20 pm, Oct 25, T.S. Michael (USNA, "Pranks by Design "), 3:30-4:05 pm, Oct 25, A. Shokrollahi , (Bell Labs, "List Decoding of Algebraic-Geometric Codes"), 4:15-4:50, Oct 25 and on Monday (in C216): Dr Charles Osgood, (NSA, "A briefing on NSA grants"), 12:00-1:00, Oct 26 Dr David Hatch, (NSA Museum, "Enigma and Purple: How the allies exploited enemy communications in WWII"), 3:45-4:45pm, Oct 26 List of speakers and titles in chronological order There are plans for a dinner with the speakers Sunday night, October 25th. Dinner with Peter Hilton on Monday night. Time and place to be announced. (Tentatively, in Annapolis somewhere, around 6pm Sunday and 5:30pm on Monday.) Directions: From Baltimore, take I97 down to Rt50, follow the signs to Annapolis. From DC, take Rt 50 east to Annapolis. Get off Rt 50 at the Rowe Blvd exit. Go straight on Rowe Blvd (through 3 lights) until you get to a T intersection. This will be Rowe+College Ave. Turn left and go to the next light. Turn right onto King George. Go straight. King George takes you to the visitors gate (also called gate 1). Visitors parking is just inside the gate to the right. (There is also a parking lot closer to the Math Dept but you should get a parking pass at gate 3 to park there.) To get to the Math Dept, go straight as you pass through the gate and follow road as it hugs the sea wall, keeping the water on your right-hand side. Eventually, you will see some sail boats docked on your right. If you go about 500 yards further, you will see a blue running track on your left. The Math Dept is in Chauvenet Hall, which is the building besides the running track. Map of USNA Map of I97 from BWI airport to USNA Several local hotels are linked to from the Capital's lodging web page. Email questions about the conference to: David Joyner Links: USNA Math Dept Homepage Math Dept Colloquium page David Joyner's Homepage Last updated 10-21-98
Algebraic and Arithmetic Geometry
(ICM 1998 Satellite Conference) Essen, Germany; 10--15 August 1998.
alg_arith.icm98 ICM 1998 SATELLITE CONFERENCE ALGEBRAIC and ARITHMETIC GEOMETRY August 10-15, 1998 Essen, Germany Third announcement There will be a satellite conference on algebraic and arithmetic geometry at the university of Essen, Germany, from August 10 until August 15, 1998. Arrival: Sunday, August 9, afternoon Departure: Saturday, August 15, afternoon Nearest airport: Dsseldorf, Germany Program: There will be plenary sessions (55 min.) and two parallel series of main lectures (45 min.), one on Geometry and one on Arithmetic. At present the following speakers accepted the invitation: V. Alexeev, V. Batyrev, K. Behrend, S. Bloch, J.-B. Bost, C. Deninger, A. Goncharov, R. Hain, D. Harbater, Y. Ihara, J. de Jong, Y. Kawamata, J. Kollr, M. Kontsevich, M. Levine, S. Mochizuki, S. Mukai, F. Oort, R. Pink, F. Pop, M. Raynaud, K. Ribet, S. Saito, T. Saito, C. Simpson, Y.-T. Siu, Ch. Soul, V. Voevodsky, S. Zhang. In addition there will be up to four parallel series of seminar talks (35 min.). The subjects of the seminars include Arithmetic and Arakelov geometry Galois theory Algebraic cycles Birational geometry Geometry and physics Projective geometry and vector bundles Preliminary schedule (new): as ps.file dvi.file tex.file Preliminary overview (new): as ps.file dvi.file tex.file Conference fee: 100,- DM. (Students without financial support 50,- DM.) Funds: available (limited, as usual...) How to find your accomodation: City map of Essen How to get to the University and to the Department of Mathematics? A short description including the addresses of the hotels: ps.file dvi.file LaTeX.file Registration: closed e-mail: icm.sat@uni-essen.de Address: ICM-Satellite Conference FB 6, Mathematik Universitt Essen D-45117 Essen, Germany Fax: 0049 201 183 2426 Organizers: H. Esnault, G. Frey, E. Viehweg (Essen), G. Faltings (Bonn) __________________________________________________________________________ Comments: mdm@exp-math.uni-essen.de Last change: August, 4 1998 Author: Michael Mller
Number Theory Day
The Centre for Applicable Analysis and Number Theory, Johannesburg, South Africa; 25 June 1997. Abstracts, photos.
Number Theory Day, Wits University, Johannesburg, South-Africa The John Knopfmacher Centre for Applicable Analysis and Number Theory Number Theory Day Conference Information and speakers Number Theory Day Programme and Titles Number Theory Day Abstracts Pretoria Number Theory Special Session Titles Pretoria Number Theory Special Session Abstracts Photos from Number Theory Day Kruger Park Trip To Centre Home Page
Workshop on Enumeration and Zeta-Functions
Lille, France; 4--6 December 1997.
Journes Cette page ne peut tre lue qu'avec un browser capable d'exploiter les frames
10th Annual Workshop on Automorphic Forms and Related Topics
Stanford, CA, USA; 27--30 March 1996.
Workshop on Automorphic Forms 10-th Annual Workshop on Automorphic Forms and Related Topics The workshop will be held from Wednesday 27 March to Sunday 30 March, 1996, at Stanford University in California, in room 380C Tentative Schedule Wednesday morning: There are cafes, bookstores and groovy shops near the hotel, and hiking in the nearby hills. Wednesday afternoon: 2:00--2:55 Scott Wolpert, "Estimation of Fourier Coefficients of nonholomorphic automorphic forms" 3:00--4:00 Yiannis Petridis, TBA 4:15--4:35 Daniel Lieman, "Bounds for the size of the Tate-Shafarevich group." 4:50--5:30 Doug Grenier, "Inhomogeneous minima and automorphic forms" Thursday: 9:30--10:10 David Cardon, "Fourier coefficients of metaplectic Eisenstein series in the function field case" 10:25--10:45 Daniel Bump, "A local Riemann hypothesis, I" 11:00--11:20 Par Kurlberg, "A local Riemann hypothesis, II" 11:35--11:55 Julie Roskies, "The minimal representation of SO(4,3)" 2:00-2:40 Cris Poor, "What vanishing order implies a Siegel modular form is zero? 2:55--3:15 Gabriel Berger, "Fake congruence subgroups" 3:30--4:10 David Joyner, TBA Friday: 9:30--10:10 Ozlem Imamoglu, TBA 10:25--11:05 Yves Martin, "On Jacobi forms of arbitrary degree and functional equations for certain Diriclet series" 11:20--12:00 Bill Duke, TBA 12:10-12:30 Sol Friedberg, "Sums of Dirichlet series" 2:00--5:00 PROBLEM SESSION which may be followed by a PARTY! Saturday: 9:30--10:30 Jiandong Guo, "Period integrals of cusp forms" 10:50--11:50 Fernando Rodriguez Villegas, TBA 2:00--3:00 Elinor Velasquez, "Toda lattices and Poincare's upper half-plane" 3:20--4:00 Jeff Stopple, "Asymptotic expansion of a heat kernel associated to Ramanujan's tau function" 4:15--4:55 Ken Ono, "Modular forms and the prime 2" Please send correspondence, including any new names and addresses to add to our annual mailing list to: walling@msri.org Back to Daniel Bump Back to Stanford Math Department
Combinatorial Number Theory
DIMACS, Rutgers University, Piscataway, NJ, USA; 5--9 February 1996.
DIMACS Workshop on Combinatorial Number Theory DIMACS Workshop on Combinatorial Number Theory February 5-9, 1996 DIMACS Center - Rutgers University Piscataway, New Jersey Workshop Announcement Call for Participation Program How to Register Information on Accommodations Information on Travel Arrangements Proceedings were not published for this workshop. Workshop Index DIMACS Homepage Contacting the Center Document last modified on July 8, 1998.
Journes des Formes Modulaires
Part of the Arithmetic Semester. English French. Lille, France; 10--12 January 2001.
Journees Formes Modulaires UFR de Mathmatiques Pures et Appliques Arithmtique - Gomtrie - Analyse - Topologie Journes des Formes Modulaires ( Dans le cadre de semestre special d'arithmtique .) 10-12 janvier 2001 Salle de Runions, Btiment M2. Mercredi 10 janvier *************************************** 10h30 : Accueil *************************************** 11h : Nils-Peter Skoruppa Quelques remarques sur le calcul des formes modulaires *************** 12h-14h Djeuner *************** 14h30 : Igor Potemine Dualit de Langlands quantique et symtrie miroir *************** 15h30 : *************** 16h : Marie-France Vigneras Groupes de Galois p-adiques, groupes lineaires p-adiques, algbres de Schur p-affines ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Jeudi 11 janvier 10h : Bernadette Perrin-Riou Fonctions L p-adiques associes a une forme modulaire *************** 11h : *************** 11h30 : Siegfried Boecherer On p-adic interpolation for triple L-functions *************** 12h30-14h30 Djeuner *************** 14h30 : Guy Henniart La correspondance locale de Langlands *************** 15h30 : *************** 16h : Ralf Schmidt A local theory of Jacobi old and newforms ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Vendredi 12 janvier 9h30 : Paul Gerardin Le theoreme de Riemann-Roch et les corps de nombres algebriques *************** 10h 30 : *************** 11h15 : Michael Harris Representations galoisiennes, representations automorphes, et varietes de Shimura *************** 12h30-14h30 Djeuner *************** 14h30 : Paula Cohen Distribution de points speciaux: questions, applications et quelques reponses 15h15 : Serguei Evdokimov Dirichlet series proportional to the spinor zeta-function of degree 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Participants Rsums Organisateurs Gautami Bhowmik : (33) 3 20 43 68 75 Valery Gritsenko : (33) 3 20 43 42 21 . Possibly useful information on Lille Subway Navigator
Journes Arithmtiques XXI
Pontificia Universitas Lateranensis, Vatican City; 12--16 July 1999.
Journes Arithmtiques - Home page "XXI Journes Arithmtiques" July 12-16, 1999 Pontificia Universitas Lateranensis Vatican City ROME, Italy The Conference The "Journes Arithmtiques" is a two yearly conference dedicated to all aspects of number theory. In 1999 the "XXI Journes Arithmtiques" will take place at the Universit Lateranense (Citt del Vaticano) in Rome (Italy) from July 12 to 16. The conference will start on Monday morning July 12, 1999 at 9:45 in the Aula Magna of the Universit Lateranense. The lectures of the invited speakers will be given in the morning. In the afternoon there are parallel sessions of short talks. There will be no talks on Wednesday afternoon, July 14. Where The Universit Lateranense is located near the Basilica San Giovanni in the center of Rome. It can easily be reached by metro and by bus. For more information on how to get to the Universit Lateranense, click here . Registration Participants are invited to register as soon as possible. This can only be done by sending in the Registration Form that is available on these web pages. The registration fee is lower for those who register before May 1, 1999. Short Communications Participants who wish to give a short talk at the "Journes Arithmtiques" were invited to submit an abstract before May 1, 1999. jabstract@mat.uniroma3.it If there are more submissions than can be accomodated, a selection will take place. Authors will be informed about the results of this selection procedure before June 1, 1999 Proceedings Just like the Proceedings of the "Journes Arithmtiques" of 1993 and 1997, the Proceedings of the "XXI Journes Arithmtiques", will be published as a volume of the " Journal de Thorie de Nombres de Bordeaux ". All speakers are invited to submit a paper for this volume before November 1, 1999. Submissions must be in TeX and will be refereed before February 1, 2000. The proceedings are expected to appear in the course of the year 2000. Details for electronic submission, format requirements and so forth will be notified in later announcements. Hotels The city of Rome attracts many visitors the whole year around. Hotel rates are very high. We strongly suggest that all participants book their accomodation as early as possible. Financial Support For young participants and participants that do not have sufficient personal resources, the conference will try to pay for part of the costs of accomodation in Rome . (If you believe that you may be eligible for some financial support, click the appropriate box on the Registration Form and fill out the form). As of April 30th, we are no longer accepting applications for financial support. The decisions concerning financial support will be made before May 1,1999. Related Scientific Activities In the weeks before the "Journes Arithmtiques" there will be a short workshop in Pisa on "Diophantine approximation and Analytic Number Theory". Immediately after the "Journes Arithmtiques" there will be a workshop at the Universit "Roma Tre" , on "Elliptic Curves, Modular Forms and Galois representations". Both activities are sponsored by INDAM . Some of these web pages are still under construction
Midwest Algebraic Number Theory Day
University of Illinois, Urbana-Champaign; 29 March 1997.
4th Midwest Algebraic Number Theory Day 4th Midwest Algebraic Number Theory Day University of Illinois, Urbana-Champaign, Saturday, March 29 The fourth Midwest Algebraic Number Theory Day will be held on Saturday, March 29, from 1 pm to 6 pm at the University of Illinois at Urbana-Champaign. The key speakers will be Richard Taylor of Harvard University and Chris Skinner of Princeton University. 1:00-1:50 Richard Taylor (Harvard), Modular forms and Galois representations 1:55-2:15 Yihsiang Liow (UIUC), Global Galois representations with prescribed local conditions 2:15-2:45 Refreshments 2:45-3:05 Darrin Doud (UIUC), S4 extensions ramified at one prime 3:10-3:50 Yuri Tschinkel (UIC), Rational points and Tamagawa numbers of algebraic varieties 3:55-4:15 Romyar Sharifi (U of Chicago), Ramification groups of nonabelian Kummer extensions 4:15-4:45 Refreshments 4:45-5:05 Boris Iskra (UIUC), Noncongruent numbers with arbitrarily many prime factors congruent to 3 (mod 8) 5:10-6:00 Chris Skinner (Princeton), Deformations of reducible representations It is hoped that people will car-pool to enable groups to drive up and back again within the day. There will be a dinner afterwards, for which people can sign up at the meeting. If anyone wishes to stay overnight, then arrangements can be made. Further details on places to stay, directions to the meeting, and a speaker roster (when available) will appear on this web page. If you intend to attend the seminar, for further information please contact me at: Nigel Boston Department of Mathematics University of Illinois Urbana, IL 61801 tel: 217-333-2677 e-mail: boston@math.uiuc.edu web: http: www.math.uiuc.edu ~boston The meeting will be held in 314 Altgeld Hall. From I-74, take the Lincoln Avenue exit. Go south for a 1.7 miles, until you reach Green Street. Go west on Green St. for 0.7 miles to 5th Street. Go south one block and then east on John. There is a free parking garage on your right at the end of the block. Altgeld Hall is the historic building with a bell tower at the end of John St., one block to the east. It's easiest to enter the building by its north face, going past the Alma Mater statue, then up to the top of the stairs to find Room 314 and the refreshment lounge. There will be signs!
Quadratic Forms 2001
Topics: algebraic theory, arithmetic theory, K-theory, algebraic groups, and the theory of metric spaces. Louisiana State University, Baton Rouge, USA; 26--30 March 2001.
Quadratic Forms 2001
Thorie d'Iwasawa des Motifs
Universit Paris 13; 28--30 March 2001.
Laboratoire d'Analyse, Gomtrie et Applications, UMR 7539 Thorie d'Iwasawa des motifs Confrence du 28 au 30 Mars 2001 Amphi Darwin, Institut Galile, Universit Paris 13 Mercredi 28 Mars 2001 R. Greenberg (U. of Washington) The structure of Galois cohomology groups I (10h) W. McCallum (U. of Arizona) On Greenberg's pseudo-null conjecture (11h30) N. Vatsal (UBC) Elliptic curves over anticyclotomic towers of number fields I (13h45) E. Urban (U. Paris 13) A propos de la conjecture de Coates-Schmidt I (15h00) K. Buzzard (Imperial College) Eigenvarieties (16h30) Jeudi 29 Mars 2001 B. Perrin-Riou (U. Paris-Sud) Croissance du groupe de Tate-Shafarevich, suite d'un travail de Kurihara (10h) G. Kings (U. Muenster) Iwasawa theory and the Bloch-Kato conjecture for Dirichlet characters (11h30) D. Delbourgo (U. of Nottingham) Coleman power series and Hida families (14h) J.-M. Fontaine (U. Paris-Sud) Reprsentations galoisiennes gomtriques sur un corps local (15h30) M. Emerton (U. of Chicago) p-adic interpolation of automorphic representations (16h45) Vendredi 30 Mars 2001 C. Cornut (U. Strasbourg) Distribution de familles de points CM (9h30) N. Vatsal (UBC) Elliptic curves over anticyclotomic towers of number fields II (11h00) E. Urban (U. Paris 13) A propos de la conjecture de Coates-Schmidt II (12h10) S. Howson (U. Paris 13) Non-abelian Iwasawa theory: Non-commutative algebra (14h15) R. Greenberg (U. of Washington) The structure of Galois cohomology groups II (16h00) Renseignements tilouine@math.univ-paris13.fr Ces confrences sont rpertories dans l' Agenda des Confrences en Mathmatiques Pour venir Cette page est : http: www-math.math.univ-paris13.fr ~gaga iwasawa.html Dernire mise jour: 24 Janvier 2001
Shimura Varieties and Automorphic Forms
Japan-U.S. Mathematics Institute, special year with Workshop and Conference 20--25 March 2001.
JAMI Home Page last updated 02 28 01. Shimura Varieties and Automorphic Forms Johns Hopkins University, Department of Mathematics Japan-U.S. Mathematics Institute Organizers: Masaaki Furusawa, Osaka City University Hiroyuki Yoshida, Kyoto University Steven Zucker, Johns Hopkins University Expected Visitors from Japan: Ken-ichi Bannai, University of Tokyo (11 1-11 30 in March) Kazuhiro Fujiwara, Nagoya University (10 1-10 22 in March) Masaaki Furusawa, Osaka City University (2 1-3 31) Kaoru Hiraga, Kyoto University (10 1-11 30 in March) Takuya Konno, Kyushu University (10 1-11 30 in March) Takuya Miyazaki, Keio University (10 2-12 21 in March) Tadashi Ochiai, University of Tokyo (10 9-10 21) Takeshi Saito, University of Tokyo (12 3-12 22 in March) Hiroyuki Yoshida, Kyoto University (10 1-10 31 in March) During the 2000-2001 academic year, weekly seminars are planned for the presentations of recent developments in the field as well as a Workshop and Conference March 20-25, 2001 to culminate the program.
Western Number Theory Conference 2000
University of San Diego, 16--20 December 2000.
index WESTERN NUMBER THEORY CONFERENCE HOMEPAGE Year 2000 Conference Information Sat. evening, Dec.16 --- Wed. morning, Dec. 20 ORGANIZERS: Stan Gurak, USD Jane Friedman, USD David Cantor, CCR Ron Evans, UCSD Email contact: David Cantor ( dgc@ccrwest.org ) Last updated: October 5, 2000
Colloquium in Honour of Professor Michel Mends France
Number Theory (analytic number theory, Diophantine approximations, uniform distribution), Combinatorics and Physics. University of Bordeaux, 11--14 September 2000.
COLLOQUIUM IN HONOR OF PROFESSOR MICHEL MENDS FRANCE COLLOQUIUM IN HONOR OF PROFESSOR MICHEL MENDS FRANCE First Announcement On the occasion of the 65th birthday of Professor Michel Mends France the university of Bordeaux will organize an International Colloquium in September 2000 (from the 11th to 14th ). The topics of the conference will be Number Theory (analytic number theory, Diophantine approximations, uniform distribution), Combinatorics and Physics. Please inform us at your earliest convenience (before end of June) whether you intend to take part in the conference. The conference fee is Fr 150 to be paid at the beginning of the conference, September 11, 2000. You may find on this link ( speakers ) the first list of invited speakers but also more detailed informations on the program of the conference ( program ) and a map to find the location of the colloquium ( map ). Please let us know if you need further information (you may also see the page information) . We expect your reply, questions and suggestions by e-mail to our address: stan@math.u-bordeaux.fr or by traditional mail to the address: Jean-Jacques Ruch Institut de Mathmatiques de Bordeaux 1 351, cours de la Libration 33405 TALENCE Cedex FRANCE You will find a registration form on the following page: registration. At the same occasion the "Journal de Thorie des Nombres de Bordeaux" will publish a volume dedicated to Michel Mends France. Every person who would like to be associated to this tribute, is invited to submit an original article to the journal . Advisory Committee: Organizing Committee: Pierre Cartier (chairman), Jean-Paul Allouche (chairman), Anne Bertrand, Christophe Doche , Jean-Marc Deshouillers, Jean-Jacques Ruch. Pierre Liardet, Jean-Franois Mla, Michel Olivier, Jacques Peyrire, This colloquium is organized by the "laboratoire de Thorie des Nombres et Algorithmique Arithmtique de l'Universit Bordeaux I ( A2X )" and is supported by Universit Bordeaux I Dpartement Sciences Physiques et Mathmatiques du CNRS GDR de Thorie Analytique des Nombres Rseau Diophante European Mathematical Society (EMS) Conseil Rgional Aquitaine Mairie de Bordeaux
CRM Montreal Theme Year 1998-99
Number Theory and Arithmetic Geometry.
CRM: Theme Year 1998-1999 Centrederecherchesmathmatiques en franais Theme Year 1998-1999 Number Theory and Arithmetic Geometry The theme year in number theory and arithmetic geometry will emphasize several current directions: Algebraic cycles and Shimura varieties, Elliptic curves and modular forms, Representations of p-adic groups, Analytic theory of automorphic L-functions. The year will be organized around a certain number of workshops, seminar courses and mini-courses spread throughout the year. Following is a schedule of events: NATO Advanced Study Institute CRM Summer School 1998: The Arithmetic and Geometry of Algebraic Cycles Workshop on Algebraic modular forms and modular forms mod p Workshop on Analytic number theory CMS Winter Meeting Workshop on Representations of reductive p-adic groups Workshop on Arithmetical algebraic geometry Moonshine Workshop 6th Conference of the Canadian Number Theory Association Seminar courses Mini-courses Chaire Aisenstadt Lectures Organizing Committee Registration Form Workshop on Algebraic modular forms and modular forms mod p 2-8 October 1998 The last decades have witnessed the emergence of a "Langlands philosophy mod p" which (among other things) relates Galois representations to modular forms mod p. This instructional workshop will survey this circle of ideas, with a special emphasis on (1) Gross's theory of "algebraic modular forms" and (2) the progress on Serre's conjectures arising from the work of Ribet, Taylor, and Wiles. There will be three lecture series. B. Gross (Harvard): Algebraic modular forms K. Ribet (UC Berkeley): Congruences between modular forms S. Kudla (Maryland): The Siegel-Weil formula Organizers: H. Darmon (McGill and CICMA) and G. Savin (Utah) Program Workshop on Analytic number theory 24-27 October 1998 The workshop will focus on recent developments in analytic number theory with special emphasis on non-vanishing theorems for L-functions attached to automorphic forms. Organizer: R. Murty (Queen's) Invited Speakers: K. Dilcher, J. Friedlander, S. Gonek, J. Hoffstein, H. Iwaniec, K. Murty, R. Murty, M. Nair, R. Raghunathan, C.S. Rajan, C. Stewart Program CMS Winter Meeting Special session in number theory (Queen's Univ., Kingston, Ontario) 13-15 December 1998 Organizers: R. Murty (Queen's) and N. Yui (Queen's) Invited Speakers: H. Darmon, C. David, J. Fabrykowski, C. Greither, H. Kisilevsky, M. Kolster, A. Ledet, C. Levesque, K. Murty, V. Platonov, D. Roy, G. Walsh, H. Williams, K. Williams Further information Workshop on Representations of reductive p-adic groups 9-13 May 1999 The main focus of the workshop will be construction of K-types for admissible representations, and Hecke algebras and their representations. Organizer: F. Murnaghan (Toronto) Invited Speakers: J. Adler, S. DeBacker, D. Goldberg, A. Helminck, C. Jantzen, P. Kutzko, D. Manderscheid, L. Morris, A. Moy, M. Reeder, B. Roberts, A. Roche, P. Sally Jr., G. Savin, J.-K. Yu Complete Schedule Workshop on Arithmetical algebraic geometry 14-18 May 1999 Arithmetic algebraic geometry covers a range of possible topics, and a number of graduate students will be attending the workshop, so participants have been asked to address their lectures to a wide audience and to attempt to deliver "survey talks". Organizers: M. Goresky (IAS) and K. Murty (Toronto) Invited Speakers: A. Baragar, D. Boyd, W. Casselman, H. Darmon, B. Gordon, M. Goresky, E. Kani, M. Kolster, J. Kramer, J. Lewis, K. Murty, M. Nori, Frans Oort, J. Scherk, N. Wieslawa, N. Yui, S.-W. Zhang Complete Schedule Moonshine Workshop 29 May - 4 June 1999 "Moonshine" started in 1978 with the observation that representations of some sporadic groups are naturally parametrized by the Fourier coefficients of certain modular forms. The functions arising here are axiomatizable as replicable functions from their behaviour under a generalized Hecke operator. There is a panoply of mathematics used in these investigations. Vertex algebras, graded Lie algebras, conformal field theory, automorphic functions, Fuchsian groups, computational algebra, Schwarz derivatives, Hecke operators, representation theory, and mirror maps all appear. The workshop, one in a two yearly series, will focus on recent developments on the subject. Organizer: J. McKay (Concordia) Invited Speakers: A.O.L. Atkin (Illinois, Chicago), A.Baker (Glasgow), S.J.Bloch (Chicago), M.Brightwell (Glasgow), J.Conway (Princeton), I.V.Dolgachev (Michigan), C.-Y.Dong (UC Santa Cruz), B.Dubrovin (SISSA, Trieste), P.Goddard FRS (Cambridge), G.I.Glauberman (Chicago), R.L.Griess Jr. (Michigan), K.Harada (Ohio State), M.J.Hopkins (M.I.T.), G.Mason (UC Santa Cruz), S.P.Norton (Cambridge), A.J.Ryba (Michigan), K.Saito (Kyoto), H.Tamanoi (UC Santa Cruz), M.Tuite (National University of Ireland, Galway), S.-T.Yau (Harvard), N.Yui (Queen's) Complete Schedule 6th Conference of the Canadian Number Theory Association (Winnipeg, Manitoba) Co-sponsored by the CRM and The Fields Institute 20-24 June 1999 Organizers: J. Borwein (Simon Fraser), D. Boyd (UBC), C. David (Concordia), R. Murty (Queen's), P. N. Shivakumar (Manitoba), C. Stewart (Waterloo), H. Williams (Manitoba) Invited Speakers: M. Bennett (IAS), F. Beukers (Utrecht), A. Bremner (Arizona State), D. Bressoud (Macalester College, MN), H. Darmon (McGill), J. Friedlander (Toronto), J. Grantham (Georgia), H. Kisilevsky (Concordia), M. Kolster (McMaster), H. W. Jenstra, Jr. (Berkeley), L. Merel (Paris), A. Odlyzko (ATT Labs, NJ), K. Ono (Penn State), B. Poonen (Berkeley), D Roy (Ottawa), P. Sarnak (Princeton), W. Schmidt (Colorado), K. Soundararajan (Princeton) G. Stevens (Boston U), S. Vanstone (Waterloo), T. Wooley (Michigan, Ann Arbor) Further information Seminar courses Seminar courses will last from one to three months. Modular forms and the Birch and Swinnerton-Dyer conjecture Lecturer: Henri Darmon (McGill and CICMA) The goal of this seminar is to survey the recent progress on the Birch and Swinnerton Dyer conjecture which follows from the work of Kolyvagin and Wiles. In particular we will try to present a complete proof of the following statement: Let E be an elliptic curve over Q whose L-function is nonzero at s=1. Then the Mordell-Weil group E(Q) is finite. Dates Times: Every Thursday, from September 17, 1998 to April 1, 1999, 8:00-10:00 Location: CRM, Univ. de Montral, Pavillon Andr-Aisenstadt, Room 5340 Elliptic and Hilbert Modular forms Speaker: Eyal Goren (CICMA, Concordia McGill) Dates Times: Every Tuesday from September 8, 1998 to April 6, 1999, 14:00-16:00 Location: CRM, Univ. de Montral, Pavillon Andr-Aisenstadt, Room 5340 The Chebotarev density theorem and some applications Speaker: Kumar Murty (Toronto) The Chebotarev Density Theorem is a fundamental tool in number theory and arithmetic geometry. We shall discuss effective versions of this theorem and some of its applications. Dates: October 9, 14, 16, 19, 21, and 30, 1998 Complete Schedule An Introduction to Sieve Methods Lecturer: Ram Murty (Queen's) This short course will survey sieve methods and some of its applications. After looking at the sieve of Eratosthenes, we will discuss the sieve methods of Brun, Selberg and Linnik. We will then examine applications of these methods to such questions as Artin's primitive root conjecture, squarefree values of polynomials, and structure of the group of points mod p of a global elliptic curve. The course will consist of a total of six lectures. Dates Times: November 5, 10, 12, 17, 19 24, 1998, 10:30-12:00 Complete Schedule Modular forms and the Birch and Swinnerton-Dyer conjecture Speaker: Henri Darmon (McGill CICMA) Dates Times: Every Thursday from January 7 to March 25, 1999, 8:30-10:00 Location: CRM, Univ. de Montral, Pavillon Andr-Aisenstadt, Room 5340 Elliptic and Hilbert Modular forms Speaker: Eyal Goren (CICMA, Concordia McGill) Dates Times: Every Tuesday from January 12 to March 30, 1999, 15:30-17:00 Location: CRM, Univ. de Montral, Pavillon Andr-Aisenstadt, Room 5340 Mini-courses There will be several mini-courses of two weeks each, spread throughout the year. Iwasawa Theory of Modular Forms Lecturer: Massimo Bertolini (Universita di Pavia) Dates Times: September 17, 22, 24 29, 1998, 10:30-12:00 Complete Schedule Ordinary Representations and Modular Forms Lecturer: Chris Skinner (Institute for Advanced Study) Dates: October 15, 20 22, 1998 Complete Schedule Rankin-Selberg L-functions Lecturer: C.S. Rajan (Tata Institute) Dates Times: November 5, 10, 12 17, 1998, 14:15-15:45 Complete Schedule Modular Forms and Modular Curves Lecturer: Imin Chen (CICMA, Concordia McGill) Dates: January 7, 12, 14 and 19, 1999 Complete Schedule Automorphic forms over function fields Lecturer: Andreas Schweizer (CICMA, Concordia McGill) January 21, 1999, McGill Univ., Burnside Hall, Room 920, 10:30-12:00 January 26, 28, February 2, 1999, Univ. de Montral, Pav. Andr-Aisenstadt, Room 5340, 10:30-12:00 Topics in p-adic Galois representations Lecturer: A. Iovita (CICMA, Concordia McGill) February 4, 1999, McGill Univ., Burnside Hall, Room 920, 10:30-12:00 February 9, 11, 16, 1999, Univ. de Montral, Pav. Andr-Aisenstadt, Room 5340, 10:30-12:00 Hilbert modular varieties Lecturer: Eyal Goren (CICMA, Concordia McGill) Timetable: February 18, 1999, McGill Univ., Burnside Hall, Room 920, 10:30-12:00 February 18, 1999, Concordia Univ., Library Building, Room LB540, 14:15-15:45 March 2, 1999, Univ. de Montral, Pav. Andr-Aisenstadt, Room 5340, 10:30-12:00 March 2, 1999, Univ. de Montral, Pav. Andr-Aisenstadt, Room 5340, 14:15-15:45 The spectrum of multiplicative values The distribution and extreme values of L-functions Lecturer: Andrew Granville (Georgia) March 4, 1999, McGill Univ., Burnside Hall, Room 920, 10:30-12:00 March 9, 11, 16, 1999, Univ. de Montral, Pav. Andr-Aisenstadt, Room 5340, 10:30-12:00 Polynomial constructions, Galois theory and elliptic curves Lecturer: Jean-Franois Mestre (Paris VII, Jussieu) March 18, 1999, McGill Univ., Burnside Hall, Room 920, 10:30-12:00 March 23, 25, 30, 1999, Univ. de Montral, Pav. Andr-Aisenstadt, Room 5340, 10:30-12:00 Representations of reductive p-adic groups Lecturer: Fiona Murnaghan (Toronto) April 20, 22, 27 29, 1999, Univ. de Montral, Pav. Andr-Aisenstadt, Room 5340, 14:00-15:30 Chaire Aisenstadt Lectures NOTE: The lectures of Professeur Andrew Wiles (Princeton), scheduled for September 1998, have been cancelled. A Series of Lectures Professor Frans Oort Universiteit Utrecht May 1999 Barsotti-Tate Groups and Newton Polygons a proof of a conjecture by Grothendieck, Montral 1970 May 14 18, 1999, 4 p.m. May 20, 25, 27 28, 1999, 2 p.m. Further Information Organizing Committee Henri Darmon (McGill and CICMA) Mark Goresky (IAS) Hershy Kisilevsky (Concordia and CICMA) Fiona Murnaghan (Toronto) Kumar Murty (Toronto) Ram Murty (Queen's), Chair Those wishing to participate in the above activities are invited to contact: Louis Pelletier CRM, Universit de Montral C.P. 6128, Succ. centre-ville Montral (Qubec) CANADA H3C 3J7 E-mail: ACTIVITES@CRM.UMontreal.CA FAX: (514) 343-2254 Telephone: (514) 343-2197 18 May 1999, webmaster@CRM.UMontreal.CA
ANTS III
3rd Algorithmic Number Theory Symposium, Reed College, Portland, Oregon; 21--25 June 1998.
ANTS: The Algorithmic Number Theory Symposium Welcome to ALGORITHMIC NUMBER THEORY SYMPOSIUM III Reed College , Portland, Oregon, USA Sunday, June 21 through Thursday, June 25, 1998 The proceedings of ANTS III have been published in a Springer Lecture Notes in Computer Science LNCS 1423 General ANTS Information Travel Accomodations Conference Schedule ANTS III Information Registration Inquiries on this conference can be directed to Joe Buhler ( jpb@reed.edu ) or Cathy D'Ambrosia ( Cathy.D.Ambrosia@reed.edu ). Information on the ANTS'98 conference - From Ant Colonies to Artificial Ants: First International Workshop on Ant Colony Optimization - in Brussels, October 15-16, 1998, can be found at ants98 .
ANTS IV
4th Algorithmic Number Theory Symposium, Leiden; 2--7 July 2000.
ANTS IV General Schedule Participants Proceedings Hotels Registration ANTS IV General Information The 4th Algorithmic Number Theory Symposium (ANTS IV) will take place in Leiden in the Netherlands the summer of the year 2000. Arrival day: Sunday July 2. The end of the conference is on Friday July 7 at 3 PM. ANTS IV will be hosted by the Mathematical Institute and the Lorentz Center of the Universiteit Leiden . The ANTS conferences, which are held every two years, are devoted to algorithmic aspects of number theory, including elementary number theory, algebraic number theory, analytic number theory, geometry of numbers, algebraic geometry, finite fields, cryptography and computational complexity. ANTS III was held in 1998 at Reed College, Portland, Oregon. Local transportation Leiden is located 25 kilometers south west of Amsterdam Airport (Schiphol). The airport is on top of a railway station having train connections to Leiden that are frequent (4 to 6 times an hour) and fast (20 minutes travel time). The Leiden railway station is walking distance from downtown Leiden, which is only a small area. You can also get a taxi at the railway station. The campus is a 20 minute walk in the other direction from the railway station and there is a bus every 30 minutes. The easiest way to get around between campus, downtown and the hotels is what all the locals do: ride a bicycle. You can rent bikes at the train station. Walking or using public transportion are also good options. There is no need to rent a car. Maps To view the conference locations you can download PNG-files of color maps small (923K), medium (3.1M) to view with a browser, and black-and white maps small (533K), medium (2.0M), large ([an error occurred while processing this directive]) for printing. The talks are in the lecture halls marked "Gorlaeus", and the welcoming reception on Sunday evening is at "Witte Huis". The buffet on Monday night is at the "Hortus Botanicus". You can print a customized map at www.mapquest.com . Welcoming reception Sunday July 2 The in-person registration will take place on Sunday July 2 from 19.00 until 21.00 at Hotel-Restaurant Het Witte Huis Wilhelminapark 33 2342 AE Oegstgeest phone 071 - 5153853 During registration, there will be a light buffet service (drinks and various snacks). You will receive your conference materials, including a copy of the proceedings (a Springer Lecture Notes in Computer Science volume). The Witte Huis is located between the Oegstgeest-exit of highway A44 and the railway station Leiden Centraal, and houses several conference participants. It can be reached by bus from the train station: take bus 31 or 41 and ask the driver to call out when you reach the "Kempenaerstraat". Now you turn left: cross the street and walk down "de Geesterlaan" for two blocks. The hotel is on your right. Dinner buffet Monday July 3 The conference dinner will take place at 7 PM in the Botanical Gardens. The entrance is on Rapenburg 73 in downtown Leiden. Special event on Wednesday July 5, 2000 Wednesday afternoon and evening will be devoted to (computations related to) the number pi. In the evening, the lost tombstone of Ludolph van Ceulen, appointed in Leiden in 1600, and famous for computing 35 decimals of pi which were engraved on his tombstone, will be replaced in the Pieterskerk (St Peter's Church) in Leiden. We originally planned to have this event on Thursday, but we had to move it to Wednesday. Speakers We have the following invited speakers Frits Beukers Peter Borwein Jin-Yi Cai Noam Elkies Victor Flynn Jacques Stern The deadline for contributed talks has passed already. The list of accepted papers is now available in Postscript. Poster The conference poster has been mailed out to a number of addresses we have on file. If you would like to receive a poster for display somewhere around you please ask us at ants4@wins.uva.nl and include your paper mail address. The poster mentions the wrong date for the Special Event: it's on Wednesday, not Thursday. Organizing committee Bart de Smit Leiden Web pages Herman te Riele CWI Jaap Top Groningen Peter Stevenhagen Amsterdam Chair Wieb Bosma Nijmegen Proceedings For further information please contact ants4@wins.uva.nl . Sponsors General Schedule Participants Proceedings Hotels Registration
Poem about the Riemann Zeta Function
A mathematical hyper-poem.
Zeta poem A poem about the Riemann zeta function My stuff: Papers Links Home AIM: AIM Home Page Where are the zeros of zeta of s ? G.F.B. Riemann has made a good guess; They're all on the critical line , saith he, And their density's one over 2 p log t. This statement of Riemann's has been like a trigger, And many good men, with vim and with vigour, Have attempted to find, with mathematical rigour, What happens to zeta as mod t gets bigger. The efforts of Landau and Bohr and Cramer, Littlewood , Hardy and Titchmarsh are there, In spite of their effort and skill and finesse, In locating the zeros there's been little success. In 1914 G.H. Hardy did find, An infinite number do lay on the line, His theorem, however, won't rule out the case, There might be a zero at some other place. Oh, where are the zeros of zeta of s? We must know exactly, we cannot just guess. In order to strengthen the prime number theorem , The integral's contour must never go near 'em. Let P be the function p minus Li, The order of P is not known for x high, If square root of x times log x we could show, Then Riemann's conjecture would surely be so. Related to this is another enigma, Concerning the Lindelf function mu sigma . Which measures the growth in the critical strip, On the number of zeros it gives us a grip. But nobody knows how this function behaves, Convexity tells us it can have no waves, Lindelf said that the shape of its graph, Is constant when sigma is more than one-half. There's a moral to draw from this sad tale of woe, which every young genius among you should know: If you tackle a problem and seem to get stuck, Use R.M.T. , and you'll have better luck. Words by Tom Apostol (revised slightly by cph). Back to Chris Hughes' home page
The Riemann Hypothesis
Web article by Aldo Peretti.
THE RIEMANN HYPOTHESIS THE RIEMANN HYPOTHESIS By Aldo Peretti Download all the text 1 Introduction In 1859, G.F.B.Riemann published a most famous paper concerning the distribution of prime numbers, with the title: On the quantity of prime numbers below a given quantity, where, for the first time were used the methods of complex variable functions in order to determine (x) : the quantity of prime numbers x. His starting formula was the product decomposition that Euler had found for the zeta function (s) = i.e. the formula (s) = where p stands for the prime numbers. (Riemann used the letter s to denote the variable, s = + it ; and this way of notation was unanimously used after him) In the first part of the memoir, he proves the functional equation of the zeta function, and after this he deduces the formula valid for 1, and where f(x) = This formula had been obtained formerly in 1848 by Tchebychev (whose work on the subject very likely was known to Riemann). But he was unable to make the inversion of this formula, that Riemann succeeded to do, obtaining thus: f(x) = ( a 1) The remaining part of Riemanns paper is very obscure and confusing because of its excessive brevity. Fortunately some years ago E.C. Edwards published a wonderful book (ref. (1)) explaining and justifying step by step Riemanns reasoning. This required about 200 pages, and put in evidence that he performed six hypotheses before arriving at his final formula: 1). There are infinitely many zeros of (s) in the critical strip 0 1. 2) The quantity N(T) of these zeros in the rectangle 0 1 0 t T is N (T) = 3) The series -2 is convergent, but -1 diverges 4) The entire function (s) = s 2 s (s-1) (s) ( s 2) admits the product decomposition 5) All the imaginary zeros have real part 1 2 6) Let where li(x) denotes the logarithmic integral function; (x) is the quantity of primes x , and denotes the imaginary zeros of the zeta function. The hypothesis 1), 3) and 4) were proved in 1892 and 1893 by Hadamard. The hypothesis 2), with error term 0(log T) was proved in 1894 by von Mangoldt, who also proved hypothesis 6) (but he used an alternative way). There is besides a numerical and irrelevant mistake in the formula for 0 (x) , where Riemann writes () instead of -log 2. Hence at present remains unproved only hypothesis 5). Remark that Riemanns formula for N(T) indeed gives the quantity of Gram points for t T, up to a difference of 8. How the hypothesis was not proved . Variant A) It is mentioned in 10.1, p. 213-214 of Titchmarshs textbook. (ref (2)) We have: This series converges very rapidly and one might suppose that an approximation to the truth could be obtained by replacing it by their first terms. The author has performed the exact calculation, and he proved that we are thus led to the formula Variant B) In other place of his book ref.(2) (Chapter III 3,1 p.38) Titchmarsh states that The problem of the zero-free region (of the zeta function) appears to be a question of extending the sphere of influence of the Euler product beyond its actual region of convergence , ...In fact, the deepest theorems on the distribution of the zeros of (s) are obtained in the way suggested. But the problem of extending the sphere of influence of (the Euler product) ... to the left of = 1 in any effective way appears to be of extreme difficulty The extremely difficulty problem was solved in 1991 by the author (ref (4)), who proved the product formula for integral positive x 2 and every s. Very unfortunately, this does not give us any information concerning the zeros. In change, in p.50 of the same reference, the author proved that there are infinitely many natural numbers x such that if there are not zeros for next EMAIL: aldo_aperetti@yahoo.es download all the text Contador Ver contador click aqui
Computation of Zeros of the Zeta Function
Verification of RH up to the 10^13-th zero, with details of the computations and further results, by Xavier Gourdon with the help of Patrick Demichel.
Computation of zeros of the Zeta function New Riemann Hypothesis verification record Riemann Hypothesis verified until the 1013-th zero. (October 12th 2004), by Xavier Gourdon with the help of Patrick Demichel. Billions of zeros at very large height (around the 1024-th zero) have also been computed. Details can be found in The 1013 first zeros of the riemann zeta function, and zeros computation at very large height . The Riemann Hypothesis (RH) is one the most important unsolved problem in mathematics (see Zeta generalities for details about the RH). It has naturally been numerically checked threw the ages, thanks to techniques about the Zeta functions evaluations (see Numerical evaluation of the Riemann Zeta-function for details). 1 History of numerical verification of the RH Numerical computations have been made threw the ages to check the RH on the first zeros. Computer age, starting with Turing computations, permitted to perform verification higher than billions of zeros. An history of the RH verification on the first n zeros is given below. Year n Author 1903 15 J. P. Gram[ 6 ] 1914 79 R. J. Backlund[ 1 ] 1925 138 J. I. Hutchinson[ 7 ] 1935 1,041 E. C. Titchmarsh[ 22 ] 1953 1,104 A. M. Turing[ 24 ] 1956 15,000 D. H. Lehmer[ 12 ] 1956 25,000 D. H. Lehmer[ 11 ] 1958 35,337 N. A. Meller[ 14 ] 1966 250,000 R. S. Lehman[ 10 ] 1968 3,500,000 J. B. Rosser, J. M. Yohe, L. Schoenfeld[ 21 ] 1977 40,000,000 R. P. Brent[ 2 ] 1979 81,000,001 R. P. Brent[ 3 ] 1982 200,000,001 R. P. Brent, J. van de Lune, H. J. J. te Riele, D. T. Winter[ 25 ] 1983 300,000,001 J. van de Lune, H. J. J. te Riele[ 8 ] 1986 1,500,000,001 J. van de Lune, H. J. J. te Riele, D. T. Winter[ 9 ] 2001 10,000,000,000 J. van de Lune(unpublished) 2004 900,000,000,000 S. Wedeniwski[ 26 ] 2004 10,000,000,000,000 X. Gourdon and Patrick Demichel[ 5 ] Notice that the latest RH verification on the first 1013 zeros have been achieved thanks to the use of the fast Zeta multi-evaluation algorithm by Odlyzko and Schnhage, and that it is the first RH verification done with this technique. Details can be found in[ 5 ]. 2 Numerical computations of the distribution of the zeros of the Zeta function While numerical computations on zeros of the Zeta function have long been focused on RH verification only (to check the RH, isolating the zeros is sufficient so no precise computations of the zeros are needed) it was Odlyzko who the first, computed precisely large consecutive sets of zeros to observe their distribution. More precisely, Odlyzko made some empirical observations of the distribution on the spacing between zeros of z(s) in various zones and checked the correspondence with the GUE hypothesis, which conjectures that normalized spacing between zeros behaves like eigenvalues of random hermitian matrices (see[ 5 ] for more details). In 1987, Odlyzko computed numerically 105 zeros of the Riemann Zeta function between index 1012+1 and 1012+105 to the accuracy of 10-8 and was the first to observe a good agreement with the GUE hypothesis (see[ 16 ]). Later, in order to reach much higher heights, Odlyzko with Schnhage[ 20 ] developed a fast algorithm for multi-evaluation of z(s). After refinements to make this method efficient for practical purposes, Odlyzko was able to compute 70 million zeros at height 1020 in 1989 and then 175 million in 1992 at the same height (see[ 17 ]). Later he reached the height 1021 (see[ 18 ]), and in 2001 he computed ten billion zeros at height 1022 (see[ 19 ]). In a more recent unpublished work in 2002, Odlyzko computed twenty billion zeros at height 1023. 3 Numerical verification of the Riemann Hypothesis on the first 1013 zeros of Zeta The algorithm of Odlyzko and Schnhage to perform efficient multi-evaluation of Zeta function was implemented by Xavier Gourdon and used to check numerically the Riemann Hypothesis on the first 1013 zeros. Details can be found in the following paper . Statistics on the first 1013 zeros of the Zeta function Close roots The smallest normalized spacing between consecutive zeros rn=1 2+ign and rn+1=1 2+ign+1, denoted by dn = (gn+1-gn) log(gn (2p) 2p has been reached at gn=1034741742903.35376 (for root index n=4,088,664,936,217), with a value of d 0.00007025. Non normalized difference between those roots is equal to 0.00001709. This is the smallest known difference between roots of the Zeta function. Other close roots have been detected while verifying the RH on the first 1013 zeros, but some of them may have been missed since they were computed only when separation of Zeta zeros were made difficult. A (non exhaustive) list of close zeros of Zeta until the 1013-th zeros in excel format can be found here : CloseRoots.xls . Gram blocks and violations of Rosser rule Complete statistics between zero of index 100,002 and the 1013-th zeros can be found here : ZetaStatGlobal_1e5_1e13.txt . The same statistics for each 1012 step are available here: Range 100,002 to 1012 . Range 1012 to 21012 . Range 21012 to 31012 . Range 31012 to 41012 . Range 41012 to 51012 . Range 51012 to 61012 . Range 61012 to 71012 . Range 71012 to 81012 . Range 81012 to 91012 . Range 91012 to 1013 . Large values of |Z(t)| No particular search or reconvergence was performed to find maximum values of |Z(t)| during the computation. The largest values encountered during evaluation were just recorded, leading to the following table : Maximum values of abs(Z(t)) encountered . 4 Computations of zeros of the Riemann Hypothesis at very large height Computation of two billion zeros of the Zeta function at each of the height 1013, 1014, , 1023 and 1024 were done. What follows is a synthetic view of what is contained in the paper paper , where the reader should refer for more details. 4.1 The GUE hypothesis While many attempts to prove the RH had been made, a few amount of work has been devoted to the study of the distribution of zeros of the Zeta function. A major step has been done toward a detailed study of the distribution of zeros of the Zeta function by Hugh Montgomery[ 15 ], with the Montgomery pair correlation conjecture. Roughly speaking, this conjecture states that the density of normalized spacing between non-necessarily consecutive zeros is 1-(sin(pu) pu)2. It was first noted by the Freeman Dyson, a quantum physicist, during a now-legendary short teatime exchange with Hugh Montgomery, that this is precisely the pair correlation function of eigenvalues of random hermitian matrices with independent normal distribution of its coefficients. Such random hermitian matrices are called the Gauss unitary ensemble (GUE). As referred by Odlyzko in[ 16 ] for example, this motivates the GUE hypothesis which is the conjecture that the distribution of the normalized spacing between zeros of the Zeta function is asymptotically equal to the distribution of the GUE eigenvalues. Under this conjecture, we might expect that the distribution of the dn itself satisfies 1 M { n : N+1 n N+M, dn [a,b]} ~ b a p(0,u)du (1) where p(0,u) is a certain probability density function, quite complicated to obtain. As reported by Odlyzko in[ 18 ], we have the Taylor expansion around zero p(0,u) = p2 3 u2 - 2p4 45 u4 + p6 315 u6 + which under the GUE hypothesis entails that the proportion of dn less than a given small value d is asymptotic to (p2 9) d3 + O(d5). Thus very close pairs of zeros are rare. Previous computations by Odlyzko[ 16 , 17 , 18 , 19 ], culminating with the unpublished result of computations at height 1023, were mainly dedicated to the GUE hypothesis empirical verifications. As observed by Odlyzko using different statistics, agreement is very good. Our goal here was to compute some of the statistics observed by Odlyzko relative to the GUE hypothesis, at height at each power of ten from 1013 to 1024. Our statistics, systematically observed at consecutive power-of-ten heights, are also oriented to observe empirically how the distribution of the spacing between zeros of the Zeta function converges to the asymptotic expectation. 4.2 Statistics The statistics here are extracted from the paper paper , with in addition the statistics files generated by our program. 4.2.1 Computation information Computation was launched on spare time of several machines. Zeros were computed starting roughly from the 10n-th zero for 13 n 24. An amount of roughly 2109 zeros was computed at each height. Physical memory requirement was less than 512 Mo, and in the case of large height (for height 1023 and 1024), an amount of 12 Go of disk space was necessary. Table below gives some indications of timing and the value of R used (see section). It is to notice that due to the difficulty to have some long spare times on the different computers used, we adapt values of R that is why it is not monotonous. Due also to different capacities of the machines, the amount of used memory were not always identical. Timings are not monotonous also but at least, the table is just here to fix idea about cost. Third and fourth columns relates to offset index, so the value 10n should be added to have the absolute index of first or last zero. First and last zeros are always chosen to be Gram points proved regular with Turing's method (see section). Height Total timing in hours offset index of first zero offset index of last zero Value of R 1013 33.1 1 2109 16777216 1014 35.0 3 2109 16777216 1015 38.3 0 2109-1 8388608 1016 49.5 1 2109-1 16777216 1017 46.9 0 2109 16777216 1018 81.6 1 2109-1 33554432 1019 65.9 0 2109+1 33554432 1020 87.8 4 2109-1 33554432 1021 139.9 0 2109-1 33554432 1022 151.5 2 2109-1 134217728 1023 219.0 100 2109-1 268435456 1024 326.6 0 2109+47 268435456 Additional timing information relates to the efficiency of our implementation, using Odlyzko-Schnhage algorithm, compared to the direct evaluation of the Zeta function using Riemann-Siegel formula(). At height 1024 for example, two third of the total time was spent in the multi-evaluation of F(t) (see section) and a single evaluation of Zeta using the direct optimized evaluation of Riemann-Siegel formula() (we used it for verification) took 5 % of the total time. So globally, the time needed to compute all the 2109 zeros at height 1024 in our implementation is approximately equal to 20 evaluations of Zeta using the direct Riemann-Siegel formula. This proves the very high efficiency of the method. 4.2.2 Distribution of spacing between zeros Statistics were done to observe numerically the agreement of asymptotic formulas( 3 ), where the function p(0,t) has been computed with modern techniques. In our statistical study to check the validity of the GUE hypothesis, we observed the agreement of the empirical data with formulas( 3 ) on each interval [a,b), with a = i 100 and b = (i+1) 100 for integer values of i, 0 i 300. In figure 1 , in addition to the curve representing the density probability function p(0,t), points were plotted at abscissa (i+1 2) 100 and coordinate ci = 100 1 M { n : N+1 n N+M,dn [i 100,(i+1) 100]}, for height N=1013 and number of zeros M @ 2 109. As we can see the agreement is very good, whereas the graphic is done with the lowest height in our collection: human eye is barely able to distinguish between the points and the curve. That is why it is interesting to plot rather the density difference between empirical data and asymptotic conjectured behavior (as Odlyzko did in[ 19 ] for example). This is the object of figure 2 , and this time what is plotted in coordinate is the difference di = ci - (i+1) 100 i 100 p(0,t)dt. To make it readable, the graphic restricts on some family of height N even if the corresponding data were computed at all height. Even if oscillations in the empirical data appear because the sampling size of 2109 zeros is a bit insufficient, we clearly see a structure in figure 2 . First, the form of the difference at each height has a given form, and then, the way this difference decreases with the height can be observed. Figure 1: Probability density of the normalized spacing dn and the GUE prediction, at height 1013. A number of 2109 zeros have been used to compute empirical density, represented as small circles. Figure 2: Difference of the probability density of the normalized spacing dn and the GUE prediction, at different height (1014, 1016, 1018, 1020, 1022, 1024). At each height, 2109 zeros have been used to compute empirical density, and the corresponding points been joined with segment for convenience. 4.2.3 Violations of Rosser rule The table below lists statistics obtained on violations of Rosser rule (VRR). As we should expect, more and more violations of Rosser rule occurs when the height increases. Special points are Gram points which are counted in a VRR, so equivalently, they are points that do not lie in a regular Gram block. Height VRR per million zeros Number of types of VRR Number of special points Average number of points in VRR 1013 37.98 68 282468 3.719 1014 54.10 86 418346 3.866 1015 72.42 109 581126 4.012 1016 93.99 140 780549 4.152 1017 117.25 171 1004269 4.283 1018 142.30 196 1255321 4.411 1019 168.55 225 1529685 4.538 1020 197.28 270 1837645 4.657 1021 225.80 322 2156944 4.776 1022 256.53 348 2507825 4.888 1023 286.97 480 2868206 4.997 1024 319.73 473 3262812 5.102 4.2.4 Behavior of S(t) The S(t) function is defined in() and permits to count zeros with formula(). It plays an important role in the study of the zeros of the Zeta function, because it was observed that special phenomenon about the zeta function on the critical line occurs when S(t) is large. For example, Rosser rule holds when |S(t)| 2 in some range, thus one needs to have larger values of S(t) to find more rare behavior. As already seen before, it is known unconditionally that S(t) = O(logt). Under the RH, we have the slightly better bound S(t) = O logt loglogt . However, it is thought that the real growth of rate of S(t) is smaller. First, it was proved that unconditionally, the function S(t) (2p2 loglogt)1 2 is asymptotically normally distributed. So in some sense, the "average" order of S(t) is (loglogt)1 2. As for extreme values of S(t); Montgomery has shown that under the RH, there is an infinite number of values of t tending to infinity so that the order of S(t) is at least (logt loglogt)1 2. Montgomery also conjectured that this is also an upper bound for S(t). As described in section 4.2.6 with formula( 5 ), the GUE suggests that S(t) might get as large as (logt)1 2 which would contradict this conjecture. As explained in[ 18 ,P. 28], one might expect that the average number of changes of sign of S(t) per Gram interval is of order (loglogt)-1 2. This is to be compared with the last column of the table below, which was obtained thanks to the statistics on Gram blocks and violations of Rosser rule. As it is confirmed in heuristic data in the table below, the rate of growth of S(t) is very small. Since exceptions to RH, if any, would probably occur for large values of S(t), we see that one should be able to reach much larger height, not reachable with today's techniques, to find those. Height Minimum of S(t) Maximum of S(t) Number of zeros with S(t) -2.3 Number of zeros with S(t) 2.3 Average number of change of sign of S(t) per Gram interval 1013 -2.4979 2.4775 208 237 1.5874 1014 -2.5657 2.5822 481 411 1.5758 1015 -2.7610 2.6318 785 760 1.5652 1016 -2.6565 2.6094 1246 1189 1.5555 1017 -2.6984 2.6961 1791 1812 1.5465 1018 -2.8703 2.7141 2598 2743 1.5382 1019 -2.9165 2.7553 3487 3467 1.5304 1020 -2.7902 2.7916 4661 4603 1.5232 1021 -2.7654 2.8220 5910 5777 1.5164 1022 -2.8169 2.9796 7322 7359 1.5100 1023 -2.8178 2.7989 8825 8898 1.5040 1024 -2.9076 2.8799 10602 10598 1.4983 4.2.5 Estimation of the zeros approximation precision As already discussed in section, a certain proportion of zeros were recomputed in another process with different parameters in the implementation and zeros computed twice were compared. Table below list the proportion of twice computed zeros per height, mean value of absolute value of difference and maximal difference. Height Proportion of zeros computed twice Mean difference for zeros computed twice Max difference for zeros computed twice 1013 4.0% 5.90E-10 5.87E-07 1014 6.0% 6.23E-10 1.43E-06 1015 6.0% 7.81E-10 1.08E-06 1016 4.5% 5.32E-10 7.75E-07 1017 8.0% 5.85E-10 9.22E-07 1018 7.5% 6.59E-10 1.88E-06 1019 11.0% 5.15E-10 3.07E-06 1020 12.5% 3.93E-10 7.00E-07 1021 31.5% 5.64E-10 3.54E-06 1022 50.0% 1.15E-09 2.39E-06 1023 50.0% 1.34E-09 3.11E-06 1024 50.0% 2.68E-09 6.82E-06 4.2.6 Extreme gaps between zeros The table below lists the minimum and maximal values of normalized spacing between zeros dn and of dn+dn+1, and compares this with what is expected under the GUE hypothesis (see section 4.1 ). It can be proved that p(0,t) have the following Taylor expansion around 0 p(0,u) = p2 3 u2 - 2 p4 45 u4 + so in particular, for small delta Prob (dn d) = d 0 p(0,u)du ~ p2 9 d3 so that the probability that the smallest dn are less than d for M consecutive values of dn is about 1- 1- p2 9 d3 M @ 1-exp - p2 9 d3 M . This was the value used in the sixth column of the table. The result can be also obtained for the dn+dn+1 Prob (dn+dn+1 d) ~ p6 32400 d8, from which we deduce the value of the last column. Height Mini dn Maxi dn Mini dn+dn+1 Maxi dn+dn+1 Prob min dn in GUE Prob min dn+dn+1 in GUE 1013 0.0005330 4.127 0.1097 5.232 0.28 0.71 1014 0.0009764 4.236 0.1213 5.349 0.87 0.94 1015 0.0005171 4.154 0.1003 5.434 0.26 0.46 1016 0.0005202 4.202 0.1029 5.433 0.27 0.53 1017 0.0006583 4.183 0.0966 5.395 0.47 0.36 1018 0.0004390 4.194 0.1080 5.511 0.17 0.67 1019 0.0004969 4.200 0.0874 5.341 0.24 0.18 1020 0.0004351 4.268 0.1067 5.717 0.17 0.63 1021 0.0004934 4.316 0.1019 5.421 0.23 0.50 1022 0.0008161 4.347 0.1060 5.332 0.70 0.61 1023 0.0004249 4.304 0.1112 5.478 0.15 0.75 1024 0.0002799 4.158 0.0877 5.526 0.05 0.19 For very large spacing in the GUE, as reported by Odlyzko in[ 18 ], des Cloizeaux and Mehta[ 4 ] have proved that logp(0,t) ~ -p2 t2 8 (t), which suggests that max N+1 n N+M dn ~ (8logM)1 2 p . (2) This would imply that S(t) would get occasionally as large as (logt)1 2, which is in contradiction with Montgomery's conjecture about largest values of S(t), discussed in section 4.2.4 . 4.2.7 Moments of spacings The table below list statistical data about moments of the spacing dn-1 at different height, that is mean value of Mk = (dn-1)k, together with the GUE expectations. Height M2 M3 M4 M5 M6 M7 M8 M9 1013 0.17608 0.03512 0.09608 0.05933 0.10107 0.1095 0.1719 0.2471 1014 0.17657 0.03540 0.09663 0.05990 0.10199 0.1108 0.1741 0.2510 1015 0.17697 0.03565 0.09710 0.06040 0.10277 0.1119 0.1759 0.2539 1016 0.17732 0.03586 0.09750 0.06084 0.10347 0.1129 0.1776 0.2567 1017 0.17760 0.03605 0.09785 0.06123 0.10407 0.1137 0.1789 0.2590 1018 0.17784 0.03621 0.09816 0.06157 0.10462 0.1145 0.1803 0.2613 1019 0.17805 0.03636 0.09843 0.06189 0.10511 0.1152 0.1814 0.2631 1020 0.17824 0.03649 0.09867 0.06215 0.10553 0.1158 0.1824 0.2649 1021 0.17839 0.03661 0.09888 0.06242 0.10595 0.1165 0.1836 0.2668 1022 0.17853 0.03671 0.09906 0.06262 0.10627 0.1169 0.1842 0.2678 1023 0.17864 0.03680 0.09922 0.06282 0.10658 0.1174 0.1850 0.2692 1024 0.17875 0.03688 0.09937 0.06301 0.10689 0.1179 0.1859 0.2708 GUE 0.17999 0.03796 0.10130 0.06552 0.11096 0.1243 0.1969 0.2902 In the next table we find statistical data about moments of the spacing dn+dn+1-2 at different height, that is mean value of Nk = (dn+dn+1-2)k, together with the GUE expectations. Height N2 N3 N4 N5 N6 N7 N8 N9 1013 0.23717 0.02671 0.16887 0.06252 0.2073 0.1530 0.3764 0.4304 1014 0.23846 0.02678 0.17045 0.06301 0.2099 0.1550 0.3827 0.4388 1015 0.23956 0.02688 0.17181 0.06349 0.2122 0.1568 0.3880 0.4458 1016 0.24050 0.02700 0.17299 0.06396 0.2142 0.1585 0.3927 0.4523 1017 0.24132 0.02713 0.17404 0.06446 0.2159 0.1601 0.3970 0.4583 1018 0.24202 0.02726 0.17494 0.06488 0.2175 0.1614 0.4005 0.4630 1019 0.24264 0.02740 0.17574 0.06530 0.2188 0.1627 0.4036 0.4672 1020 0.24319 0.02753 0.17645 0.06569 0.2201 0.1639 0.4065 0.4713 1021 0.24366 0.02766 0.17709 0.06609 0.2212 0.1651 0.4092 0.4753 1022 0.24409 0.02778 0.17765 0.06643 0.2222 0.1660 0.4114 0.4780 1023 0.24447 0.02790 0.17819 0.06679 0.2232 0.1671 0.4140 0.4821 1024 0.24480 0.02801 0.17863 0.06709 0.2240 0.1679 0.4158 0.4846 GUE 0.249 0.03 0.185 0.073 0.237 0.185 0.451 0.544 The last table below is about mean value of logdn, 1 dn and 1 dn2. Height logdn 1 dn 1 dn2 1013 -0.101540 1.27050 2.52688 1014 -0.101798 1.27124 2.53173 1015 -0.102009 1.27184 2.54068 1016 -0.102188 1.27235 2.54068 1017 -0.102329 1.27272 2.54049 1018 -0.102453 1.27308 2.54540 1019 -0.102558 1.27338 2.54906 1020 -0.102650 1.27363 2.54996 1021 -0.102721 1.27382 2.54990 1022 -0.102789 1.27401 2.54783 1023 -0.102843 1.27415 2.55166 1024 -0.102891 1.27427 2.55728 GUE -0.1035 1.2758 2.5633 4.2.8 Statistic files The following files contains, in a "brute" form, the global statistics of our computation of two billion non trivial zeros of the Riemann zeta function, at different height (zero number 10n for 13 n 24). Each file corresponds to one height, and contains data like Gram blocks, types and number of violations of Rosser rule, extremal values of deltan and dn+dn+1 (dn is the normalized gap between consecutive zeros), data on S(t), moments on dn, and observed distributions on gaps. Height 1013 . Height 1014 . Height 1015 . Height 1016 . Height 1017 . Height 1018 . Height 1019 . Height 1020 . Height 1021 . Height 1022 . Height 1023 . Height 1024 . References [1] R.J. Backlund. Uber die nullstellen der Riemannschen zetafunktion. Dissertation, 1916. Helsingfors. [2] R.P. Brent. The first 40,000,000 zeros of z(s) lie on the critical line. Notices of the American Mathematical Society, (24), 1977. [3] R.P. Brent. On the zeros of the Riemann zeta function in the critical strip. Mathematics of Computation, (33):1361-1372, 1979. [4] J.des Cloizeaux and M.L. Mehta. Asymptotic behavior of spacing distributions for the eigenvalues of random matrices. J. Math. Phys., 14:1648-1650, 1973. [5] Xavier Gourdon. The 1013 first zeros of the Riemann zeta function, and zeros computation at very large height. available at http: numbers.computation.free.fr Constants Miscellaneous zetazeros1e13-1e24.pdf, October 2004. [6] J.P. Gram. Note sur les zros de la fonction de Riemann. Acta Mathematica, (27):289-304, 1903. [7] J.I. Hutchinson. On the roots of the Riemann zeta function. Transactions of the American Mathematical Society, 27(49-60), 1925. [8] H.J. J. teRiele J.vande Lune. On the zeros of the Riemann zeta function in the critical strip. iii. Mathematics of Computation, 41(164):759-767, October 1983. [9] H.J. J. teRiele J.vande Lune and D.T. Winter. On the zeros of the Riemann zeta function in the critical strip. iv. Math. Comp., 46(174):667-681, April 1986. [10] R.S. Leghman. Separation of zeros of the Riemann zeta-function. Mathematics of Computation, (20):523-541, 1966. [11] D.H. Lehmer. Extended computation of the Riemann zeta-function. Mathematika, 3:102-108, 1956. [12] D.H. Lehmer. On the roots of the Riemann zeta-function. Acta Mathematica, (95):291-298, 1956. [13] M.L. Mehta and J.des Cloizeaux. The probabilities for several consecutive eigenvalues of a random matrix. Indian J. Pure Appl. Math., 3:329-351, 1972. [14] N.A. Meller. Computations connected with the check of Riemanns hypothesis. Doklady Akademii Nauk SSSR, (123):246-248, 1958. [15] H.L. Montgomery. The pair correlation of zeroes of the zeta function. In Analytic Number Theory, volume24 of Proceedings of Symposia in Pure Mathematics, pages 181-193. AMS, 1973. [16] A.M. Odlyzko. On the distribution of spacings between zeros of the zeta function. Mathematics of Computation, 48:273-308, 1987. [17] A.M. Odlyzko. The 1021-st zero of the Riemann zeta function. note for the informal proceedings of the Sept. 1998 conference on the zeta function at the Edwin Schroedinger Institute in Vienna., Nov. 1988. [18] A.M. Odlyzko. The 1020-th zero of the Riemann zeta function and 175 million of its neighbors. Available at URL= http: www.dtc.umn.edu ~odlyzko unpublished index.html, 1992. [19] A.M. Odlyzko. The 1022-th zero of the Riemann zeta function. In M.van Frankenhuysen and M.L. Lapidus, editors, Dynamical, Spectral, and Arithmetic Zeta Functions, number 290 in Contemporary Math. series, pages 139-144. Amer. Math. Soc., 2001. [20] A.M. Odlyzko and A.Schnhage. Fast algorithms for multiple evaluations of the Riemann zeta-function. Trans. Amer. Math. Soc., (309), 1988. [21] J.B. Rosser, J.M. Yohe, and L.Schoenfeld. Rigorous computation and the zeros of the Riemann zeta-function. In Information Processing, number68 in Proceedings of IFIP Congress, pages 70-76. NH, 1968. [22] E.C. Titchmarsh. The zeros of the Riemann zeta-function. In Proceedings of the Royal Society of London, volume 151, pages 234-255, 1935. [23] C.A. Tracy and H.Widom. Introduction to random matrices. In G.F. Helminck, editor, Geometric and Quantum aspects of integrale systems, volume 424 of Lecture Notes in physics, pages 103-130, Berlin, Heidelberg, 1993. Springer. [24] A.M. Turing. Some calculations of the Riemann zeta-function. In Proceedings of the Royal Society of London, number3, pages 99-117, 1953. [25] R.P. BrentJ. van de Lune H. J. J.te Riele and D.T. Winter. On the zeros of the Riemann zeta function in the critical strip. ii. Mathematics of Computation, 39(160):681-688, October 1982. [26] S.Wedeniwski. Zetagrid - computational verification of the Riemann hypothesis. In Conference in Number Theory in Honour of Professor H.C. Williams, Alberta, Canda, May 2003. Back to numbers, constants and computation File translated from TEX by TTH , version 3.40. On 24 Oct 2004, 22:33.
The Riemann Hypothesis
Article by Enrico Bombieri (PDF) and video by Jeff Vaaler (.ram) from the Clay Mathematics Institute.
Clay Mathematics Institute Clay Mathematics Institute Dedicated to increasing and disseminating mathematical knowledge HOME | ABOUT CMI | PROGRAMS | NEWS EVENTS | AWARDS | SCHOLARS | PUBLICATIONS Riemann Hypothesis Some numbers have the special property that they cannot be expressed as the product of two smaller numbers, e.g., 2, 3, 5, 7, etc. Such numbers are called prime numbers, and they play an important role, both in pure mathematics and its applications. The distribution of such prime numbers among all natural numbers does not follow any regular pattern, however the German mathematician G.F.B. Riemann (1826 - 1866) observed that the frequency of prime numbers is very closely related to the behavior of an elaborate function (s) = 1 + 1 2s + 1 3s + 1 4s + ... called the Riemann Zeta function. The Riemann hypothesis asserts that all interesting solutions of the equation (s) = 0 lie on a certain vertical straight line. This has been checked for the first 1,500,000,000 solutions. A proof that it is true for every interesting solution would shed light on many of the mysteries surrounding the distribution of prime numbers. The Millennium Problems Official Problem Description Enrico Bombieri Problems of the Millennium: The Riemann Hypothesis (2004) Peter Sarnak Lecture by Jeff Vaaler at the University of Texas (video) Facsimile of Riemann's 1859 manuscript Return to top Contact | Search | Terms of Use | Clay Mathematics Institute
Proof of Riemann's Hypothesis
A claimed proof of Riemann's Hypothesis.
Proof of Riemann's Hypothesis PROOF OF RIEMANN'S HYPOTHESIS James Constant math@coolissues.com Riemann's hypothesis is proved using Riemann's functional equation. Introduction The famous conjecture known as Riemann' s hypothesis 1 is to classical analysis what Fermat's last theorem is to arithmetic. Euler (1737) noted that the formula the sum extending to all positive integers n, and the product to all positive primes p. The necessary conditions of convergence hold for complex values of s with real part 1. Considering as a function of of the complex variable s, Riemann (1859) proved that satisfies a functional equation = which led Riemann to the theorem that all the zeros of , except those at s=-2,-4,-6, . . . , lie in the strip of the s-plane for which where x is the real part of s. Riemann conjectured that all the zeros in the strip should lie on the line x= . Attempts to prove or disprove this conjecture have generated a vast and intricate department of analysis, especially since Hardy (1914) proved that has an infinity of zeros on x= . 2 The question is still open in 2000. A prize is available to prove or disprove Riemann's hypothesis. 3 Proof Using Riemann's Functional Equation It has already been shown that all zeros are in the critical strip and that they are symmetric about the critical line x= . 4 Riemann's functional equation can be restated as =A( in which A( 0 at all points in the critical strip. Since functions and are single valued at each point in the critical strip they can be written in terms of their real and imaginary parts =u + iv and =u' + iv' in which ................ ................ On the critical line x= and =A( in which s~ is the conjugate of s. Thus, if =0 on the critical line then , since u=u'=0 and v=v'=0, =0 and Riemann's functional equation is satisfied. At all other points in the critical strip x and A( . Thus, if =0 in the critical strip where x then, since u u' and v v', 0 and Riemann's functional equation cannot be satisfied. Riemann's functional equation, therefore, precludes zeros at points where x in the critical strip. All zeros in the critical strip are on the critical line x . 1 See Chris Caldwell's The Riemann Hypothesis (University of Tennessee at Martin) at http: www.utm.edu research primes notes rh.html 2 E.T. Bell, The Development of Mathematics, Dover Publications, New York 1972. page 315. 3 See Enrice Bombieri's The Riemann Hypothesis (Clay Mathematics Institute) at http: www.claymath.org prize_problems riemann.htm 4 See note 1 above. Copyright 2003 by James Constant By the same author: Proof of Fermat's Last theorem at http: fermat.coolissues.com fermat.htm Is Fermat's Last Theorem Proven? at http: wiles.coolissues.com wiles.htm Some Extended Zeta Functions Provide Easy Proofs of Riemann's Hypothesis at http: zeta.coolissues.com zeta.htm Finding Prime Numbers at http: fprimes.coolissues.com fprimes.htm Algebraic Factoring of the Cryptography Modulus and Proof of Goldbach's Conjecture http: goldbach.coolissues.com goldbach.htm Proof of the Twin Primes Conjecture http: tprimes.coolissues.com tprimes.htm
Easy Proof of Riemann's Hypothesis
Generalisations of the zeta function might provide a proof of Riemann's hypothesis.
Body Some Extended Zeta Functions Provide Easy Proofs of Riemann's Hypothesis James Constant math@coolissues.com While extended zeta functions support investigations of Riemann's hypothesis and estimates for the Prime Number Theorem, some zeta functions offer better prospects for providing easy proofs. Definitions A first zeta function is defined by .................... oo (1) ...... z(s)= ....................................s=x+jy........ x 1 ................... n=1 A second zeta function is defined by ....................... oo (2) ......z(1-s)= ...............................s=x+jy........ x 0 ...................... n=1 In 1859, Riemann had the idea to define z(s) for all complex numbers s by analytic extension. This extension is important in number theory and plays a central role in the distribution of prime numbers. There are a number of ways of extending the zeta function to points where 0 x 1. 1 One way of extending is by using the first f function alternating series defined by 2 .................... oo (3) ...... f(s)= ............................ s=x+jy ........ x 0 ................... n=1 which provides an extension of the first zeta function (1) to values of z such that 0 x 1 by means of the formula (4) ...... f(s)=(1-2 )z(s) ....................... x 1 A second f function is defined by ....................... oo (5) ...... f(1-s)= ......................... s=x+jy ........ x 1 ...................... n=1 which provides an extension of the second zeta function (2) to values of z such that 0 x 1 by means of the formula (6) ...... f(1-s)=(1-2 )z(1-s) .................... x 0 Equations (1) through (6) are analytic. Riemann's Extended Zeta Function and Functional Equation Euler (1737) noted that the formula (7) ...... for integers s 1 connected integers and primes, the sum extending to all positive integers n, and the product to all positive primes p. Considering as a function of z(s) of the complex variable s, Riemann (1859) examined this equation for s as a complex number and found that it can be extended to points with real part s 1 by the formula (among others) 3 (8) ...... z(s)= which function is another form of an extended Riemann zeta function. Riemann also proved that his extended zeta function (8) satisfies a functional equation (among others) (9) ...... z(s) = z(1-s) ........ s=x+jy which led him to the theorem that all the zeros of z(s), except those at s=-2,-4,-6, . . . , lie in the critical strip of the s-plane for which where x is the real part of s. Riemann conjectured that all the zeroes in the critical strip should lie on the critical line x=1 2. 4 Attempts to prove or disprove this conjecture have generated a vast and intricate department of analysis, especially since Hardy (1914) proved that z(s) has an infinity of zeros on x=1 2. 5 The question is still open in 2001. A prize is available to prove or disprove Riemann's hypothesis. 6 Riemann's extended zeta function (8) is probably one reason it has proven difficult to investigate Riemann's hypothesis. While the function is analytic, it is difficult to express it as a complex number with real and imaginary parts. This is not the case for the extended zeta or f function of equation (3). I will now show how equation (3) is a better extended zeta function for investigating Riemann's hypothesis. I note that Riemann's functional equation (9) can be expressed as the ratio z(s) z(1-s)=C(s) and that, but for some function B(s), z(s) z(1-s)= B(s)f(s) f(1-s) which can now be used in equation (9) to produce a new functional equation (10) ...... f(s)=A(s)f(1-s) the importance of which is that the f-functions can be easily expressed as complex numbers with real and imaginary parts. Elsewhere, I attempt a proof of Riemann's hypothesis using Riemann's extended zeta function (8). 7 , Here, I use extended zeta function (3) to make the proof. Proving Riemann's Hypothesis My theory for proving Riemann's hypothesis is simple. Since, f(s) f(1-s), except when x=1 2, functional equation (10) precludes zeros in the critical strip, except when x=1 2. I now show that f(s)=f(1-s)=0 only on the critical line x=1 2. It has already been shown that all zeros are in the critical strip and that they are symmetric about the critical line x=1 2. 8 Riemann's functional equation (9) can be restated in terms of the new functional equation (10) in which A(s) 0 at all points on the critical strip. Since functions f(s) and f(1-s) are single valued at each point on the critical strip they can be written in terms of their real and imaginary parts f(s)=u+jv and f(1-s)=u'+jv' in which .................. oo .............................................. oo (11) ...... u= ................v=- ................. n=1 ............................................ n=1 .................. oo ............................................. oo .............. u'= ................v'= ................. n=1 ........................................... n=1 When sin(ylnn)=0, equations (11) reduce to .................. oo (12) ...... u= ................v=0 ................. n=1 .................. oo .............. u'= .............. v'=0 ................. n=1 which occur when (13) yn,k= , .....n=1,2,3,...., .....k=0,1,2,3,....., sin(yn,klnn)=0, ......cos(yn,klnn)=(-1)k The significance of result (13) is that it gives, for each n, the (infinite) values of y for which v=v'=0 and thus greatly simplifies extended zeta f functions (3) and (5). It remains to be shown that equations (12) put the zeros of u and u' exactly on the critical line x=1 2. These equations now become .......................... oo (14) ...... u=(-1)k (-1)n+1 ......................... n=1 .......................... oo ............. u'=(-1)k .......................... n=1 Equations (14) are conditionally convergent infinite series which, depending from the rearrangement of terms, can be divergent or convergent to some number including zero. In such series, the value of the sum of the series can be changed at will by suitable rearraingement of the series. 9 Non-zero values of each series occur in the critical strip 0 x 1 even when x=1 2. Zero values mean that the value of each series, in the limit, approaches zero u0 and u'0. Since the difference between the sum of a converging alternating series and the sum of the first n terms is numerically less than the (n+1)th term and . Thus, as noo and uu'0, x1-x and x1 2 which proves Riemann's hypothesis in the sense that, in the limit, zeros of f(s)=f(1-s) approach but never reach the critical line x=1 2. A more rigorous proof puts zeros exactly on the critical line x=1 2 and nowhere else. Formally, since A(s) in functional equation (10) is determinate at all points of the critical strip including when x=1 2, f(s) and f(1-s) are different functions at all points of the critical strip except when x=1 2 and sin(ylnn)=0 for which f(s)=f(1-s)=0. This proves Riemann's hypothesis in the sense that zeros exist only on the critical line x=1 2. For example, if zeros exist on either side of and on x=1 2, then A(s)=f(s) f(1-s)=0 0 and, thus, A(s) is indeterminate at all points of the critical strip including when x=1 2, a result precluded by determinate A(s) in equation (10). Note that, since sin(ylnn)=0, y is not a single point but a collection of double infinite numbers yn,k on the critical line. In summary: 1. Equation (10) dictates that f(s)=f(1-s) on the critical line; 2. Equation f(s)-f(1-s)=0 dictates that sin(ylnn)=0 on the critical line; and 3. Equations (11) through (14) dictate that f(s)=f(1-s)=0 on the critical line, thus proving Riemann's hypothesis. The Prime Number Theorem and Riemann's Hypothesis The prime number theorem states that the number of primes p(x) in an interval x is approximately p(x)~x lnx where lnx is the natural logarithm of x. This theorem was proved by Hadamard (1896) and independently by de la Valle Pousson (1896) using Riemann's hypothesis, after showing that the zeros of Riemann's zeta function z(s) cannot lie too far off the critical line. Also assuming that the Riemann hypothesis is true, von Koch (1901) proved that ................................................................................. oo (15) ...... p(x)=Li(x)+O(x2logx) ................... Li(x)= ................................................................................ 2 where L(i) is Gauss's integral and O(x2logx) is an error term. 10 Thus, if Riemann's hypothesis is true, equation (15) tells us that Li(x) is a very good approximation to p(x). The known values of p(x) today agree with equation (15) but it is admitted that it is not easy to "have an idea of what should be exactly the error term." 11 . Here, results (13) and (14) should be helpful. 1 See E.C. Titchmarsh, The theory of the Riemann Zeta-function, Oxford Science Publications, second edition, revised by D.R.Heath-Brown (1986). 2 See R. Courant, Differential and Integral Calculus, Interscience Publishers, Inc. New York 1947 Vol. II page 568 problem 13. 3 See "The Rieman Hypothesis in a Nutshell" at http: www.math.ubc.ca ~pugh RiemannZeta RiemannZetaLong.html 4 See Chris Caldwell's "The Riemann Hypothesis" (University of Tennessee at Martin) at http: www.utm.edu research primes notes rh.html 5 See E.T. Bell, The Development of Mathematics, Dover Publications, New York 1972. Page 315. 6 See Enrice Bombieri's "The Riemann Hypothesis" (Clay Mathematics Institute) at http: www.claymath.org prize_problems riemann.htm 7 See my Proof of Riemann's Hypothesis at http: riemann.coolissues.com rieman.htm 8 See endnote 4 above. 9 See R. Courant, Differential and Integral Calculus, Interscience Publishers, Inc. New York, 1947 2d ed. Vol. I pages 372-375. 10 See pages 5-7 in Chris Caldwell's "How Many Primes Are There" at http: www.utm.edu research primes howmany shtml 11 See "The Riemann's Zeta Function z(s)" at http: numbers.computation.free.fr Constant Primes counting Primes.html _________________________________ By the same author: Proof of Fermat's Last theorem at http: fermat.coolissues.com fermat.htm Proof of Riemann's Hypothesis at http: rieman.coolissues.com riemann.htm Finding Prime Numbers at http: findprimenumbers.coolissues.com fprimes.htm Algebraic Factoring of the Cryptography Modulus and Proof of Goldbach's Conjecture http: findprimenumbers.coolissues.com goldbach.htm Copyright by James Constant 2003
The Riemann Hypothesis
Some of the conjectures and open problems concerning RH, compiled by the AIM.
The Riemann Hypothesis This web page highlights some of the conjectures and open problems concerning The Riemann Hypothesis. If you would like to print a hard copy of the whole outline, you can download a dvi , postscript or pdf version. What is an $L$-function? Terminology and basic properties Functional equation Euler product $\xi$ and $Z$ functions Critical line and critical strip Trivial zeros Zero counting functions Arithmetic L-functions The Riemann zeta function Dirichlet L-functions Dedekind zeta functions GL(2) L-functions Dirichlet series associated with holomorphic cusp forms Examples Dirichlet series associated with Maass forms Higher rank L-functions The Selberg class Dirichlet series Analytic Continuation Functional Equation Euler Product Ramanujan Hypothesis Selberg Conjectures Analogues of zeta-functions Dynamical zeta-functions Spectral zeta functions Riemann Hypotheses Riemann Hypotheses for global L-functions The Riemann Hypothesis The Generalized Riemann Hypothesis The Extended Riemann Hypothesis The Grand Riemann Hypothesis Other statements about the zeros of L-functions Quasi Riemann Hypothesis The Density Hypothesis 100 percent hypothesis Zeros on the $\sigma=1$ line Landau-Siegel zeros The vertical distribution of zeros The Lindelof hypothesis and breaking convexity Perspectives on RH Analytic number theory Physics Probability Fractal geometry Equivalences to RH Primes The error term in the PNT More accurate estimates Arithmetic functions Averages The von Mangoldt function The M\"obius function Large values The sum of divisors of $n$ The Euler function The maximal order of an element in the symmetric group The Farey series Mikolas functions Amoroso's criterion Weil's positivity criterion Li's criterion Bombieri's refinement Complex function theory Speiser's criterion Logarithmic integrals An inequality for the logarithmic derivative of xi Function spaces The Beurling-Nyman Criterion A mollification problem Salem's criterion Other analytic estimates M. Riesz series Hardy-Littlewood series Newman's criterion Polya's integral criterion Grommer inequalities Dynamical systems Redheffer's matrix Attacks on the Riemann Hypothesis Alain Connes's approach The dynamical system problem studied by Bost--Connes The C*-algebra of Bost--Connes Iwaniec' approach families of rank 2 elliptic curves Unsuccessful attacks on the Riemann Hypothesis Zeros of Dirichlet polynomials de Branges' positivity condition Zeta Gallery Anecdotes about the Riemann Hypothesis The individual participant contributions may have problems because converting complicated TeX into a web page is not an exact science. The dvi, ps, or pdf versions are your best bet.
Zetagrid
Numerical verification of the Riemann Hypothesis by a collaborative computing effort, with downloadable software.
ZetaGrid Homepage ZetaGrid ZetaGrid Acknowledgement Performance characteristics Riemann Hypothesis Prizes Motivation News Statistics Software Publications Forum Links This site is owned by Sebastian Wedeniwski Sponsors IBM Deutschland Entwicklung GmbH Webhosting powered by EDIS.at Do you need help? Try the ZetaGrid forum What is ZetaGrid? ZetaGrid is a platform independent grid system that uses idle CPU cycles from participating computers. Grid computing can be used for any CPU intensive application which can be split into many separate steps and which would require very long computation times on a single computer. ZetaGrid can be run as a low-priority background process on various platforms like Windows, Linux, AIX, Solaris, HP-UX, and Mac OSX. On Windows systems it may also be run in screen saver mode. ZetaGrid in practice: At the IBM Development Laboratory in Bblingen ZetaGrid solves one problem in practice, running on six different platforms: The verification of Riemann's Hypothesis is considered to be one of modern mathematics most important problems. This implementation involves more than 11,000 workstations and has a peak performance rate of about 7056 GFLOPS. More than 1 billion zeros for the zeta function are calculated every day. To learn more about ZetaGrid, you have two options: view grid monitoring data and statistics of the current implementation on our performance page. participate in the calculation of zeros for the Riemann zeta function and download the client code from our software page to be one of our top producers who maybe wins a prize . Technical details: ZetaGrid provides a secure Java kernel, which does not allow access from the outside, and secures its communications and activities by restricted layer access with digital signatures (ElGamal public-key encryption) and key establishment protocols (half-certified Diffie-Hellman and ElGamal key agreement). The keys have a length of 1024 Bits. The framework of ZetaGrid provides management capabilities and is easy to use. Furthermore, it is supported on different platforms and has been proven to be stable. See the following documents for more details. Verification of Riemann's Hypothesis Currently participating: 11,894 computers : 8,373 x86 on Windows 2,775 x86 on Linux 1,955 ppc on AIX 380 ia64 on Linux 111 ppc on Mac OS X 80 sparc on SunOS 14 amd64 on Linux 11 ppc on Linux 11 alpha on Linux 7 sparc on Linux 5 s390 on Linux 5 PA_RISC2.0 on HP-UX 2 x86 on SunOS 1 amd64 on Windows 1 i386 on FreeBSD 1 ia64 on Windows Performance ~1076 GFLOPS Top team (last 7 days) CPUTOASTERS 4 active members delivered 98,300,000 zeros used 9 computer(s) Top producer (last 7 days) Robert Heinzen delivered 84,700,000 zeros used 17 computer(s) Active producer (random of last 24 h) Kelvin Lee delivered 2,600,000 zeros used 2 computer(s)
Riemann Hypothesis in a Nutshell
An article by Glen Pugh with a Java applet for viewing zeta on the critical line.
Riemann Hypothesis in a Nutshell [ Home ] [ Z(t) Plotter ] [ Verifying RH ] [ More Applets ] The Riemann Hypothesis in a Nutshell The Riemann Zeta Function image source In his 1859 paper On the Number of Primes Less Than a Given Magnitude, Bernhard Riemann (1826-1866) examined the properties of the function for s a complex number. This function is analytic for real part of s greater than 1 and is related to the prime numbers by the Euler Product Formula , again defined for real part of s greater than one. This function extends to points with real part s less than or equal to one by the formula (among others) . The contour here is meant to indicate a path which begins at positive infinity, descends parallel to and just above the real axis, circles the origin once in the counterclockwise direction, and then returns to positive infinity parallel to and just below the real axis. This function is analytic at all points of the complex plane except the point s = 1 where it has a simple pole. This last function is the Riemann Zeta Function (the zeta function). The Riemann Hypothesis The zeta function has no zeros in the region where the real part of s is greater than or equal to one. In the region with real part of s less than or equal to zero the zeta function has zeros at the negative even integers; these are known as the trivial zeros. All remaining zeros lie in the strip where the real part of s is strictly between 0 and 1 (the critical strip). It is known that there are infinitely many zeros on the line 1 2 + it as t ranges over the real numbers. This line in the complex plane is known as the critical line. The Riemann Hypothesis (RH) is that all non-trivial zeros of the zeta function lie on the critical line. Let's say that again: Riemann Hypothesis: all non-trivial zeros of the zeta function lie on the line 1 2 + it as t ranges over the real numbers. The Functional Equation and Friends The functional equation of the zeta function is from which values of the zeta function at s can be computed from its values at 1-s . Using this equation one sees immediately that the zeta function is zero at the negative even integers. Multiplying this equation through by s(s-1) 2 and applying standard factorial identities shows that is an entire function which has as zeros the non-trivial zeros of the zeta function, and is invariant under the transformation s - 1-s . This invariance and the fact that the function is real for real s implies that it is also real on the critical line s = 1 2 + it , t real. On this line s = 1 2 + it , . The first term in this last equation is always negative. The second term, denoted Z(t), is real and has the same zeros as the zeta function at 1 2 + it , t real. Thus locating zeros on the critical line of the (complex) zeta function reduces to locating zeros on the real line of the real function Z(t). The Z(t) term in the previous equation may be expressed where . For computational purposes, the expansion is used. This function converges very rapidly for t at all large. The function Z(t) is typically the object of study for locating zeros of the zeta function on the critical line and verifying the Riemann Hypothesis . The Z(t) Plotter Sorry, but the applet doesn't want to run for some reason The applet to the left is a real time plot of t vs. Z(t) for t 100 . With this little tool you can view the behaviour of Z(t) and spot its zeros visually, not to mention entertain yourself by watching the seemingly random oscillations of the curve. The applet should work fine for t up to 10,000,000 or so, though it is much smoother and faster for smaller ( ~100,000 ) values of t . Even for t around 1,000,000,000 the applet does the right thing, though the animation reduces to a sequence of snapshots. A more serious consideration is that the numerical accuracy is questionable at these large t values. Notice that as you try larger values of t , say t = 1,000,000 or so, the density of the zeros increases. The tic marks on the t -axis are called Gram Points, which are by definition points at which the theta function takes on integral multiples of pi. These also increase in density with increasing t , and for the most part, the zeros of Z(t) alternate with the Gram points. This alternation of zeros with Gram points is key to verifying the Riemann Hypothesis . The algorithm used to compute Z(t) is called the Riemann-Siegel formula, after B. Riemann who first discovered though did not publish it, and C. Siegel (1896-1981) who finally deciphered Riemann's notes and published the result in the 1930's. This algorithm is quite efficient relative to other known methods, requiring order t1 2 operations to compute each value of Z(t) . Prior to Siegel's rediscovery, the most popular method was Euler-Maclaurin Summation which requires order t operations per evaluation of Z(t) . One interesting fact about the Z(t) curve is that the absence of a zero between consecutive local extrema would signal a counter-example to the Riemann Hypothesis (RH). Occasionally the curve very nearly fails to cross the t -axis before changing direction, offering a tantalizing suggestion that perhaps RH is false. Take a look at t = 17143.8 for example. This near failure of RH is known as Lehmer's Phenomenon. About the Applet I've tried to write the Java code using only JDK 1.0 classes and methods so that it works on most browsers, in particular the older ones. The decimal formatting is still kind of iffy, and there is some odd behaviour when you zoom or change t values on the fly, but otherwise it works ok. If the applet does not work for you, please drop me a note and tell me what browser you're using and what kind of errors you're getting. The applet seems to work much more smoothly in the Java Appletviewer than within a browser. If you have this tool, try viewing this web page in it using for eg: [prompt%] appletviewer http: www.this.web.page (in Unix Linux anyway). Verifying the Riemann Hypothesis Basic Strategy Since there are infinitely many non-trivial zeros of the zeta function , there is no way you can verify computationally that they all lie on the critical line . You can, however, verify the validity of the Riemann Hypothesis in large bounded subsets of the critical strip . The standard strategy for verifying the Riemann Hypothesis up to height T is to count all of the zeros of Z(t) for 0 t T ; and compute an upper bound on the number of zeros of the zeta function which lie in the critical strip and have imaginary part between zero and T . If the results from these two steps match, then RH holds up to height T . Before going too much into detail, you may want to have a look at the Z(t) Plotter Java applet which will help with the explanations to follow. Counting Zeros and Gram's Law The approach to counting zeros of Z(t) is that used by J.Gram (1850-1916) based on a very simple observation. Recall that . Gram observed that the real part of the zeta function on the critical line tends to be positive, while the imaginary part alternates more regularly between positive and negative values. That means that the sign of Z(t) must be opposite to that of the sine function most of the time, so one would expect the zeros of Z(t) to alternate with zeros of the sine term, i.e. when theta takes on an integer multiples of pi. This turns out to hold most of the time and is known as Gram's Law. (a law which is violated infinitely often though!) The values t where theta takes on integer multiples of pi are called Gram points, and Gram's Law is the statement that zeros of Z(t) alternate with the Gram points. Define the nth Gram point gn to be the (unique) point such that . Then Gram's Law is . Gram points which satisfy Gram's Law are called good, while those that don't are called bad (not surprisingly.) A Gram block is an interval [gn, gn+k) such that gn and gn+k are good Gram points and all Gram points inside the interval are bad. The exercise of counting zeros then reduces to that of counting all Gram points where Gram's law is satisfied, and adding to that the count of zeros inside each Gram block. With this process you don't have to locate zeros exactly, you just have to compute Z(t) accurately enough to show that it changes sign. Turing to the Rescue Now that you've located a few million zeros of the zeta function on the critical line, you would like to show somehow that these are in fact all of the zeros in the region 0 t T you examined. Enter A.Turing (1912-1954). Turing devised an ingenious method of determining the number of roots in the critical strip up to height T . Define S(T) by where N(T) is the number of roots in the critical strip between zero and T . Turing showed that . This is useful because if gm is a Gram point where Gram's law is satisfied, it turns out that S(gm) must be an even integer. This integral forces |S(gm)| 2 under the right conditions, from which |S(gm)| = 0 and . Showing that |S(gm)| 2 is not a lot of work, though the argument used is a bit technical. An interesting property of the argument is that it relies solely on values of Z(t) for t real. In other words, under the right circumstances, counting the number of zeros of the zeta function in the critical strip to height T depends only on its values on the critical line. Some Results To date the methods above have been used to verify RH to large heights of the critical strip. Van de Lune et al. have shown that the first one and half billion non-trivial zeros lie on the critical line, while A. Odlyzko has demonstrated the validity of RH in large regions of the critical strip near the 1020 th zero. As part of my Master's project, I used these methods on my PC to show that the first twelve million or so zeros of the zeta function lie on the critical line (big surprise!) RH Related Applets Here are a few other applets related to the zeta function and the prime number theorem: Riemann Zeta Function Animation - zeta(1 2+it) in the complex plane Dirichlet Series Animation - wandering partial sums psi(x) Animation - convergence of Von Mangoldt's psi(x) formula [ Home ] [ Top of Page ]
The Riemann Hypothesis
A short article with some grahpical and numerical evidence in the critical strip.
riemann The Riemann Hypothesis is currently the most famous unsolved problem in mathematics. Like the Goldbach Conjecture (all positive even integers greater than two can be expressed as the sum of two primes), it seems true, but is very hard to prove. I did some playing around with the Riemann Hypothesis, and I'm convinced it is true. My observations follow. The Zeta Function Euler showed that z(2) = p2 6 , and solved all the even integers up to z(26). See the Riemann Zeta Function in the CRC Concise Encyclopedia of Mathematics for more information on this. It is possible for the exponent s to be Complex Number (a + b I). A root of a function is a value x such that f(x) = 0. The Riemann Hypothesis : all nontrivial roots of the Zeta function are of the form (1 2 + b I). Mathematica can plot the Zeta function for complex values, so I plotted the absolute value of z(1 2 + b I) and z(1 3 + b I). |z(1 2 + b I)| for b = 0 to 85. Note how often the function dips to zero. |z(1 3 + b I)| for b = 0 to 85. Note how the function never dips to zero. The first few zeroes of |z(1 2 + b I)| are at b = 14.1344725, 21.022040, 25.010858, 30.424876, 32.935062, and 37.586178. Next, I tried some 3D plots, looking dead on at zero. The plot of the function looked like this: Plot3D[Abs[Zeta[y+ x I]],{x,5,200},{y,.4,.6},PlotRange - {0,.1}, PlotPoints - 200, ViewPoint- {200,.5,0}] It seems like |z(a + b I)| is bounded away from zero when a doesn't equal 1 2. Based on these plots and a few others, I'm fairly certain the Riemann Hypothesis is true. The person who actually proves the hypothesis will be as famous as Andrew Wiles (he proved Fermat's Last Thereom). By the analytic convergence theorem, we can get the slope: z'(x + q I) = . Is it true that Re(z'(x + q I)) 0 for x 1 2 and Re(z'(x + q I)) 0 for x 1 2 ? May 4 2002 -- The first ten billion zeroes are on the critical line, 1 2.
The Riemann Hypothesis
A short article by Kimon Spiliopoulos.
The Riemann Hypothesis The Riemann Hypothesis Riemann's Hypothesis was one of the 23 problems - milestones that David Hilbert suggested in 1900, at the 2nd International Conference on Mathematics in Paris, that they should define research in mathematics for the new century (and indeed, it is not an exaggeration to say that modern mathematics largely come from the attempts to solve these 23 problems). It is the most famous open question today, especially after the proof of Fermat's Last Theorem . The Riemann zeta function is of central importance in the study of prime numbers. In its first form introduced by Euler, it is a function of a real variable x: This series converges for every x 1 (for x=1 it is the non-corvergent harmonic series). Euler showed that this function can also be expressed as an infinite product which involves all prime numbers pn, n=1, : Riemann studied this function extensively and extended its definition to take complex arguments z. So the function bears his name. Of particular interest are the roots of : Trivial zeros are at z= -2, -4, -6, Nontrivial zeros are at z such that 0 Re(z) 1 and there are infinite ones. Infinitely many lie in particular on Re(z)=1 2 (proved in 1914 by the English number theorist Godfrey Hardy) There are no zeros for Re(z) 1. The case Re(z)=1 was proved in 1896 by Hadamard and de la Valle-Poussin and used in their proof of the Prime Number Theorem . Riemann conjectured that all nontrivial zeros are at Re(z)=1 2. Although this has been shown to be true for more than the first billion nontrivial zeros, the conjecture remains open. A proof would establish new results in number theory, for example on the distribution of primes. The fact that Riemann Hypothesis holds for billions of nontrivial zeros does not guarantee anything. As noted by I. Good and R. Churchhouse in 1968, in the theories of zeta function and of primes distribution, one frequently meets terms like log log x, a function which increases extremely slow. The first nontrivial root not on Re(1 2) might have an imaginary part y such that log log y is of the order say 10. Then y would be 1010,000, a definitely unreachable number, computationally. See also the relevant page in Chris Caldwell's Prime Pages . Famous Problems and Proofs Main Page
Riemann Hypothesis
Article with links to other resources from MathWorld.
Riemann Hypothesis -- From MathWorld INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News (RSS) New in MathWorld MathWorld Classroom Interactive Entries Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Calculus and Analysis Special Functions Riemann Zeta Function Number Theory Number Theoretic Functions Number Theoretic Sums Calculus and Analysis Complex Analysis General Complex Analysis Calculus and Analysis Roots Foundations of Mathematics Mathematical Problems Unsolved Problems Foundations of Mathematics Mathematical Problems Prize Problems Recreational Mathematics Mathematics in Film and Literature Mathematics in Films A Beautiful Mind (2001) Recreational Mathematics Mathematics in Film and Literature Mathematics in Television NUMB3RS Episode 5 MathWorld Contributors Sondow MathWorld Contributors Wedeniwski Riemann Hypothesis First published by Riemann (1859), the Riemann hypothesis states that the nontrivial Riemann zeta function zeros , i.e., the values of other than -2, -4, -6, ... such that (where is the Riemann zeta function ) all lie on the " critical line " (where denotes the real part of ). While it was long believed that Riemann's hypothesis was the result of deep intuition on the part of Riemann , an examination of his papers by C. L. Siegel showed that Riemann had made detailed numerical calculations of small zeros of the Riemann zeta function to several decimal digits (Granville 2002; Borwein and Borwein 2003, p. 68). A more general statement known as the generalized Riemann hypothesis conjectures that neither the Riemann zeta function nor any Dirichlet L-series has a zero with real part larger than 1 2. The Riemann hypothesis has thus far resisted all attempts to prove it. Stieltjes (1885) published a note claiming to have proved the Mertens conjecture with , a result stronger than the Riemann hypothesis and from which it would have followed. However, the proof itself was never published, nor was it found in Stieltjes papers following his death, so it is strongly believed his claim to have possessed such a proof was erroneous (Derbyshire 2004, pp. 160-161 and 250). In the late 1940s, H. Rademacher's erroneous proof of the falsehood of Riemann's hypothesis was reported in Time magazine, even after a flaw in the proof had been unearthed by Siegel (Borwein and Bailey 2003, p. 97; Conrey 2003). de Branges has written a number of papers discussing a potential approach to the generalized Riemann hypothesis (de Branges 1986, 1992, 1994) and in fact claiming to prove the generalized Riemann hypothesis (de Branges 2003, 2004; Boutin 2004), but no actual proofs seem to be present in these papers. Furthermore, Conrey and Li (1998) prove a counterexample to de Branges's approach, which essentially means that theory developed by de Branges is not viable. Proof of the Riemann hypothesis is number 8 of Hilbert's problems and number 1 of Smale's problems . In 2000, the Clay Mathematics Institute ( http: www.claymath.org ) offered a $1 million prize ( http: www.claymath.org millennium Rules_etc ) for proof of the Riemann hypothesis. Interestingly, disproof of the Riemann hypothesis (e.g., by using a computer to actually find a zero off the critical line ), does not earn the $1 million award. The Riemann hypothesis has been computationally tested and found to be true for the first 200000001 zeros (Brent et al. 1982, which covered zeros in the region ). More recently, S. Wedeniwski uses ZetaGrid, an internal computer cluster of IBM Corporation combined with external computations compiled on http: www.zetagrid.net to prove that the first nontrivial zeros of the lie on the critical line. This computation verifies that the Riemann hypothesis is true at least for all . The Riemann hypothesis is equivalent to the statement that all the zeros of the Dirichlet eta function (a.k.a. the alternating zeta function) (1) falling in the critical strip lie on the critical line . Wiener showed that the prime number theorem is literally equivalent to the assertion that the Riemann zeta function has no zeros on (Hardy 1999, pp. 34 and 58-60; Havil 2003, p. 195). In 1914, Hardy proved that an infinite number of values for can be found for which and (Havil 2003, p. 213). However, it is not known if all nontrivial roots satisfy . Selberg (1942) showed that a positive proportion of the nontrivial zeros lie on the critical line , and Conrey (1989) this to at least 40% (Havil 2003, p. 213). Andr Weil proved the Riemann hypothesis to be true for field functions (Weil 1948, Eichler 1966, Ball and Coxeter 1987). In 1974, Levinson (1974ab) showed that at least 1 3 of the roots must lie on the critical line (Le Lionnais 1983), a result which has since been sharpened to 40% (Vardi 1991, p. 142). It is known that the zeros are symmetrically placed about the line . This follows from the fact that, for all complex numbers , 1. and the complex conjugate are symmetrically placed about this line. 2. From the definition (1), the Riemann zeta function satisfies , so that if is a zero, so is , since then . It is also known that the nontrivial zeros are symmetrically placed about the critical line , a result which follows from the functional equation and the symmetry about the line . For if is a nontrivial zero, then is also a zero (by the functional equation), and then is another zero. But and are symmetrically placed about the line , since , and if , then . The Riemann hypothesis is equivalent to , where is the de Bruijn-Newman constant (Csordas et al. 1994). It is also equivalent to the assertion that for some constant , (2) where is the logarithmic integral and is the prime counting function (Wagon 1991). Another equivalent form states that (3) where (4) where is the fractional part (Balazard and Saias 2000). By modifying a criterion of Robin (1984), Lagarias (2000) showed that the Riemann hypothesis is equivalent to the statement that (5) for all , with equality only for , where is a harmonic number and is the divisor function (Havil 2003, p. 207). The plots above show these two functions (left plot) and their difference (right plot) for up to 1000. There is also a finite analog of the Riemann hypothesis concerning the location of zeros for function fields defined by equations such as (6) This hypothesis, developed by Weil, is analogous to the usual Riemann hypothesis. The number of solutions for the particular cases , (3,3), (4,4), and (2,4) were known to Gauss . According to Fields medalist Enrico Bombieri, "The failure of the Riemann hypothesis would create havoc in the distribution of prime numbers" (Havil 2003, p. 205). In Ron Howard's 2001 film A Beautiful Mind , John Nash (played by Russell Crowe) is hindered in his attempts solve the Riemann hypothesis by the medication he is taking to treat his schizophrenia. SEE ALSO: Berry Conjecture , Critical Line , Critical Strip , Dirichlet Eta Function , Extended Riemann Hypothesis , Generalized Riemann Hypothesis , Li's Criterion , Mertens Conjecture , Mills' Constant , Prime Number Theorem , Riemann Zeta Function , Riemann Zeta Function Zeros , Robin's Theorem . [PagesLinkingHere] REFERENCES: Balazard, M. and Saias, E. "The Nyman-Beurling Equivalent Form for the Riemann Hypothesis." Expos. Math. 18, 131-138, 2000. Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 75, 1987. Bombieri, E. "Problems of the Millennium: The Riemann Hypothesis." http: www.claymath.org millennium Riemann_Hypothesis Official_Problem_Description.pdf . Borwein, J. and Bailey, D. Mathematics by Experiment: Plausible Reasoning in the 21st Century. Natick, MA: A. K. Peters, pp. 66-68, 2003. Boutin, C. "Purdue Mathematician Claims Proof for Riemann Hypothesis." Purdue News Release. June 8, 2004. http: news.uns.purdue.edu UNS html4ever 2004 040608.DeBranges.Riemann.html . Brent, R. P. "On the Zeros of the Riemann Zeta Function in the Critical Strip." Math. Comput. 33, 1361-1372, 1979. Brent, R. P.; van de Lune, J.; te Riele, H. J. J.; and Winter, D. T. "On the Zeros of the Riemann Zeta Function in the Critical Strip. II." Math. Comput. 39, 681-688, 1982. Caldwell, C. K. "Prime Links++." http: primes.utm.edu links theory conjectures Riemann . Clay Mathematics Institute. "The Riemann Hypothesis." http: www.claymath.org millennium Riemann_Hypothesis . Conrey, J. B. "At Least Two Fifths of the Zeros of the Riemann Zeta Function Are on the Critical Line." Bull. Amer. Math. Soc. 20, 79-81, 1989. Conrey, J. B. "More than Two Fifths of the Zeros of the Riemann Zeta Function Are on the Critical Line." J. reine angew. Math. 399, 1-26, 1989. Conrey, J. B. "The Riemann Hypothesis." Not. Amer. Math. Soc. 50, 341-353, 2003. http: www.ams.org notices 200303 fea-conrey-web.pdf . Conrey, J. B. and Li, X.-J. "A Note on Some Positivity Conditions Related to Zeta- and -Functions." 3 Dec 1998. http: arxiv.org abs math.NT 9812166 . Csordas, G.; Smith, W.; and Varga, R. S. "Lehmer Pairs of Zeros, the de Bruijn-Newman Constant and the Riemann Hypothesis." Constr. Approx. 10, 107-129, 1994. de Branges, L. "The Riemann hypothesis for Hilbert Spaces of Entire Functions." Bull. Amer. Math. Soc. 15, 1-17, 1986. de Branges, L. "The Convergence of Euler Products." J. Func. Anal. 107, 122-210, 1992. de Branges, L. "A Conjecture Which Implies the Riemann Hypothesis." J. Func. Anal. 121, 117-184, 1994. de Branges, L. "Apology for the Proof of the Riemann Hypothesis." March 18, 2003. http: www.math.purdue.edu ftp_pub branges apology.pdf . de Branges, L. "Riemann Zeta Functions." May 24, 2004. http: www.math.purdue.edu ftp_pub branges riemannzeta.pdf . du Sautoy, M. The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics. New York: Harper-Collins, 2003. Eichler, M. Introduction to the Theory of Algebraic Numbers and Functions. New York: Academic Press, 1966. Granville, A. "Prime Possibilities and Quantum Chaos." 2002. http: www.msri.org ext Emissary EmissarySpring02.pdf. Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, 1999. Havil, J. "The Riemann Hypothesis" and "Why Is the Riemann Hypothesis Important?" 16.10 and 16.11 in Gamma: Exploring Euler's Constant. Princeton, NJ: Princeton University Press, pp. 202-207, 2003. Krantz, S. G. "The Riemann Hypothesis." 13.2.9 in Handbook of Complex Variables. Boston, MA: Birkhuser, p. 161, 1999. Lagarias, J. C. "An Elementary Problem Equivalent to the Riemann Hypothesis" 22 Aug 2000. http: arxiv.org abs math.NT 0008177 . Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 25, 1983. Levinson, N. "More than One Third of Zeros of Riemann's Zeta-Function Are on ." Adv. Math. 13, 383-436, 1974. Levinson, N. "At Least One Third of Zeros of Riemann's Zeta-Function Are on ." Proc. Nat. Acad. Sci. USA 71, 1013-1015, 1974. Odlyzko, A. "The th Zero of the Riemann Zeta Function and 70 Million of Its Neighbors." Pegg, E. Jr. and Weisstein, E. W. "Seven Mathematical Tidbits." MathWorld Headline News. Nov. 8, 2004. http: mathworld.wolfram.com news 2004-11-08 seventidbits 3 . Riemann, G. F. B. "ber die Anzahl der Primzahlen unter einer gegebenen Grsse." Monatsber. Knigl. Preuss. Akad. Wiss. Berlin, 671-680, Nov. 1859. Reprinted in Das Kontinuum und Andere Monographen (Ed. H. Weyl). New York: Chelsea, 1972. Robin, G. "Grandes valeurs de la fonction somme des diviseurs et hypothse de Riemann." J. Math. Pures Appl. 63, 187-213, 1984. Sabbagh, K. Dr. Riemann's Zeros: The Search for the $1 Million Solution to the Greatest Problem in Mathematics. Atlantic Books, 2002. Sloane, N. J. A. Sequences A002410 M4924 in "The On-Line Encyclopedia of Integer Sequences." Smale, S. "Mathematical Problems for the Next Century." Math. Intelligencer 20, No. 2, 7-15, 1998. Smale, S. "Mathematical Problems for the Next Century." In Mathematics: Frontiers and Perspectives 2000 (Ed. V. Arnold, M. Atiyah, P. Lax, and B. Mazur). Providence, RI: Amer. Math. Soc., 2000. Stieltjes, T. C. R. A. S. 1885. te Riele, H. J. J. "Corrigendum to: On the Zeros of the Riemann Zeta Function in the Critical Strip. II." Math. Comput. 46, 771, 1986. van de Lune, J. and te Riele, H. J. J. "On The Zeros of the Riemann Zeta-Function in the Critical Strip. III." Math. Comput. 41, 759-767, 1983. van de Lune, J.; te Riele, H. J. J.; and Winter, D. T. "On the Zeros of the Riemann Zeta Function in the Critical Strip. IV." Math. Comput. 46, 667-681, 1986. Vardi, I. Computational Recreations in Mathematica. Reading, MA: Addison-Wesley, 1991. Wagon, S. Mathematica in Action. New York: W. H. Freeman, p. 33, 1991. Weil, A. Sur les courbes algbriques et les varits qui s'en dduisent. Paris, 1948. Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, p. 28, 1986. ZetaGrid Homepage. http: www.zetagrid.net . CITE THIS AS: Eric W. Weisstein. "Riemann Hypothesis." From MathWorld --A Wolfram Web Resource. http: mathworld.wolfram.com RiemannHypothesis.html 1999 CRC Press LLC, 1999-2005 Wolfram Research, Inc. | Terms of Use
Riemann's Hypothesis
A beginners guide by Jon Perry.
Riemann's Hypothesis Riemann's Hypothesis [Home] [Other Maths] [Riemann's Hypothesis Part 2] My proof of Riemann's Hypothesis Riemann's Hypothesis Euler's zeta function Euler's zeta function, which forms the basis for Riemann's Hypothesis, is the sum of the integers from 1 to infinity raised to a complex power. It is written: This converges for complex s such that the real part of s is greater than 1, but for s =1 it diverges, and is not considered to be valid on this region. Riemann's zeta function Riemann had the idea to extend this function into the whole complex plane, which he managed to do, except for a simple pole at s=1. He achieved this through a process called analytic continuation. Analytic continuation is whereby an alternative function is used that behaves exactly as the original function in the domain of the original function, and continues the function outside of the original domain. This is the idea in defining i2=-1. The previous definition of square root did not allow for square root of negative numbers, and i is the analytic continuation of the square root function. With analytic continuation, we can have different expressions for the zeta function, but they all behave the same. This is similar to writing either sigma(1 ns), and its equivalents pi2 6, and product(1-1 pis). Each one is a different expression, but they all have the same value. As said before, Riemann extended the zeta function so that it is valid in almost all of the complex plane. As it happens, this is not entirely necessary, as it has been proved that any zeroes of the zeta function (which is what we are interested in) lie in a 'critical strip', which is the area where 0 s 1. An example of extending the zeta function into s 0 is: {x} is the fractional part of x, i.e. x-[x], where [x] is the integer part of x. The derivation of this is fairly lengthy - see [here] Another approach is to consider an alternating zeta function: We can split this into two sums, one sums the zeta function, and the other removes the negative terms. After re-arranging this, we arrive at: As the alternating zeta function converges for s 0, we have found a new method for expressing the original zeta function. This new zeta function has zeroes, and these form the basis for the Riemann Hypothesis. There are trivial zeroes at -2,-4,-6, etc,... and the rest lie on the line s=1 2 + it. Or so it is thought. To solve Riemann's Hypothesis is therefore to prove that all the non-trivial zeroes do lie on this line. This has been validated for large numbers of zeroes, and it is also known that 40% of the zeroes do lie on this line, and that there are an infinite number of zeroes. Riemann originally extended the domain of the zeta function to the whole complex plane (except for a simple pole at 1), but it suffices to extend it to s 0. (we are only interested in s=1 2 - it has been proved that all the zeroes lie in the 'critical strip' 0 s 1) Finding zeroes Finding the zeroes of the zeta function is a complex task, and requires numerical techniques. The whole scenario boils down to a waveform that travels along the s=1 2 line. It has peaks and troughs, and if all the zeroes are on the critical line (s=1 2), then the peaks and troughs will always be on opposite sides of the critical line. zeta(s) defines a function that takes complex values and returns complex values. A zero therefore occurs when the returned value has both real and imaginary parts zero. It is possible for either the real or imaginary part to be equal to zero by itself, but these 'semi-zeroes' are of less interest. [picture generated with UBASIC. Download UBASIC ] This graph is demonstrating where the zeta zeroes are. The vertical axis is the real numbers, and 0.0 is representing the s=1 2 line, although the rest of the numbers do not make much sense (the zeta equation is very difficult to handle, and numerous transforms are made on the data to achieve usable results). The horizontal axis is the imaginary axis. So, Riemann's zeta function has zeroes at 14.13 (to 2dp - it is conjectured that all zeta zeroes are irrational), 21.02, 25.01, and so on. The complete list of zeta zeroes to 100, and with a higher dp count, is: Zero number Imaginary component 1 14.1347251417347 2 21.0220396387715 3 25.0108575801457 4 30.4248761258595 5 32.9350615877392 6 37.5861781588256 7 40.9187190121475 8 43.3270732809150 9 48.005150881167 10 49.773832477672 11 52.9703214777144 12 56.446247697063 13 59.3470440026022 14 60.8317785246098 15 65.112544048081 16 67.0798105294942 17 69.546401711174 18 72.0671576744819 19 75.7046906990839 20 77.14484006887479 21 79.3373750202493 22 82.9103808540860 23 84.735492980517 24 87.425274613125 25 88.809111207634 26 92.491899270550 27 94.6513440405198 28 95.8706342282453 29 98.8311942181937 Also note that the zeroes are reflected in the x-axis, i.e. if s+it is a zero, then s-it is also. Possible failure of the Riemann Hypothesis Riemann's hypothesis would fail if a single counterexample was found, so what is needed is a proof that this: never happens (i.e. a peak or trough happens out of sync). There are several close calls, where a peak or trough is very close to the x-axis, but to date no complete miss. Transforming the complex plane This is an image of the points in the [0,1]*[0,20] region (R*Ri) after having being transformed by the zeta function: We can clearly see dots in the region of (0,0). Click [here] for more images of the zeta function. Deriving the prime numbers from the zeta zeroes The relationship between the zeta zeroes and the prime numbers is not immediately obvious. To establish a connection, we need to consider the psi function introduced by Chebyshev. lambda(x) is logp if x=pk, and 0 otherwise. Essentially, psi(x) represents the number of primes and prime powers less than x. psi(x) is asymtopic to x, but the important feature is that the zeroes of the zeta equation can be used to generate accurate approximatations to the psi0(x) formula. psi0(x) is similar to psi(x), but is defined differently at discontinuites. Each rho represents a zeta zero. As more zeroes are used, the RHS tends to psi0(x). Note that rho covers all the zeroes, i.e. those with a positive and negative imaginary component. As these form complex conjugates, the imaginary part of psi0(x) is always zero. A picture of Riemann Please address questions comments suggestions to : Jon Perry
The Riemann Hypothesis
A prime pages article by Chris K. Caldwell.
The Riemann Hypothesis The Riemann Hypothesis (Another of the Prime Pages ' resources) Home Search Site Largest The 5000 Finding How Many? Mersenne Glossary Prime Curios! Prime Lists FAQ e-mail list Titans Prime Links Submit primes Summary: When studying the distribution of prime numbers Riemann extended Euler's zeta function (defined just for s with real part greater than one) to the entire complex plane (sans simple pole at s = 1). Riemann noted that his zeta function had trivial zeros at -2, -4, -6, ... and that all nontrivial zeros were symmetric about the line Re(s) = 1 2. The Riemann hypothesis is that all nontrivial zeros are on this line. In 1901 von Koch showed that the Riemann hypothesis is equivalent to: The Riemann Hypothesis: Euler studied the sum for integers s 1 (clearly (1) is infinite). Euler discovered a formula relating (2k) to the Bernoulli numbers yielding results such as and . But what has this got to do with the primes? The answer is in the following product taken over the primes p (also discovered by Euler): Euler wrote this as Riemann later extended the definition of (s) to all complex numbers s (except the simple pole at s=1 with residue one). Euler's product still holds if the real part of s is greater than one. Riemann derived the functional equation of the Riemann zeta function: where the gamma function (s) is the well-known extension of the factorial function ( (n+1) = n! for non-negative integers n): (Here the integral holds if the real part of s is greater than one and the product holds for all complex numbers s.) The Riemann zeta function has the trivial zeros at -2, -4, -6, ... (the poles of (s 2)). Using the Euler product (with the functional equation) it is easy to show that all the other zeros are in the critical strip of non-real complex numbers with 0 = Re(s) = 1, and that they are symmetric about the critical line Re(s)=1 2. The unproved Riemann hypothesis is that all of the nontrivial zeros are actually on the critical line. In 1986 it was shown that the first 1,500,000,001 nontrivial zeros of the Riemann zeta function do indeed have real part one-half [ VTW86 ]. Hardy proved in 1915 that an infinite number of the zeros do occur on the critical line and in 1989 Conrey showed that over 40% of the zeros in the critical strip are on the critical line [ Conrey89 ]. However, there is still a chance that the Riemann hypothesis is false. In August of 2001, Sebastian Wedeniwski began ZetaGrid , a distributed project that has greatly extended these computations (take a look, you might want to help out). In 1900 Hilbert listed proving or disproving this hypothesis as one of the most important unsolved problems confronting modern mathematics. When Hadamard and de la Vallee Poussin proved the prime number theorem , they actually showed for some positive constant a. The error term depended on what was known about the zero-free region of the Riemann zeta function within the critical strip. As our knowledge of the size of this region increases, the error term decreases. In 1901 von Koch showed that the Riemann hypothesis is equivalent to: Another prime page by Chris K. Caldwell caldwell@utm.edu
The Riemann Hypothesis
Notes by Steven Finch.
Mathematical Constants Mathematical Constants by Steven R. Finch Clay Mathematics Institute Book Fellow My website is smaller than it once was. Please visit again, however, since new materials will continue to appear occasionally. * My book Mathematical Constants is now available for online purchase from Cambridge University Press (in the United Kingdom and in North America ). It is far more encompassing and detailed than my website ever was. It is also lovingly edited and beautifully produced - many thanks to Cambridge! - please support us in our publishing venture. Thank you. (If you wish, see several very kind reviews . You can also search the book via Amazon and Google by keyword.) Here are errata and addenda to the book (last updated 11 15 2005), as well sample essays from the book about integer compositions , optimal stopping and Reuleaux triangles . Here also are recent supplementary materials, organized by topic: Number Theory and Combinatorics Bipartite, k-colorable and k-colored graphs (6 5 2003) Transitive relations, topologies and partial orders (6 5 2003) Series-parallel networks (7 7 2003) Two asymptotic series (12 10 2003) Multiples and divisors (1 27 2004) Discrepancy and uniformity (2 19 2004) Unitarism and infinitarism (2 25 2004) Erds' minimum overlap problem (7 2 2004) Planar graph growth constants (8 25 2004) Tauberian constants (8 30 2004) Integer partitions (9 22 2004) Class number theory (5 26 2005) Quadratic Dirichlet L-series (7 15 2005) Elliptic curves over Q (10 10 2005) Modular forms on SL2(Z) (11 15 2005) Riemann zeta moments Inequalities and Approximation Hardy-Littlewood maximal inequalities (10 12 2003) Bessel function zeroes (10 23 2003) Nash's inequality (11 4 2003) Uncertainty inequalities (11 7 2003) Airy function zeroes (7 19 2004) Projections of minimal norm (11 30 2004) Bohr's inequality (12 5 2004) Moduli of continuity (12 22 2004) Real and Complex Analysis Radii in geometric function theory (1 5 2004) Numerical radii of linear operators (4 5 2005) Coefficient estimates for univalent functions (12 15 2004) Planar harmonic mappings (3 29 2005) Constant of interpolation (4 5 2005) Probability and Stochastic Processes Hammersley's path process (4 5 2004) Moments of sums (4 23 2004) Ornstein-Uhlenbeck process (5 15 2004) Zero crossings (5 19 2004) Variants of Brownian motion (6 12 2004) Shapes of binary trees (6 24 2004) Expected lifetimes and inradii (2 23 2005) Geometry and Topology Knots, links and tangles (8 8 2003) Convex lattice polygons (12 18 2003) Volumes of hyperbolic 3-manifolds (9 5 2004) Poisson-Voronoi tessellations (3 11 2005) Optimal escape paths (5 30 2005) Minkowski-Siegel mass constants (1 9 2005) Slicing problem (4 5 2005) Constant of Theodorus (4 9 2005) I mention several favorite links: Mathematical Constants and Computation (by X. Gourdon and P. Sebah), MathWorld Constants (by E. Weisstein at Wolfram Research), and the Inverse Symbolic Calculator Integer Relations (both at CECM). My former employer, MathSoft Inc., has posted my (ancient) draft notes for the book here and here . Here is contact information for me. I appreciate your interest! * In October 2002, an unnamed third party demanded that this website be shut down, and I had no choice but to comply. I am grateful to Cambridge University Press and to INRIA Rocquencourt for patiently seeing me through a difficult time (up to June 2003).
Papers on Zeros of the Riemann Zeta Function
By Andrew Odlyzko.
zeta.html Andrew Odlyzko: Papers on Zeros of the Riemann Zeta Function and Related Topics (see also "Tables of zeros of the zeta function" and "Some unpublished materials" on the main home page) The 10^22-nd zero of the Riemann zeta function, A. M. Odlyzko. Dynamical, Spectral, and Arithmetic Zeta Functions, M. van Frankenhuysen and M. L. Lapidus, eds., Amer. Math. Soc., Contemporary Math. series, no. 290, 2001, pp. 139-144. [Abstract] [PostScript] [PDF] [LaTeX] An improved bound for the de Bruijn-Newman constant, A. M. Odlyzko, Numerical Algorithms, 25 (2000), pp. 293-303. [Abstract] [PostScript] [PDF] [LaTeX] A nonlinear equation and its application to nearest neighbor spacings for zeros of the zeta function and eigenvalues of random matrices, P. J. Forrester and A. M. Odlyzko, in Organic Mathematics, J. Borwein, P. Borwein, L. Jorgenson, and R. Corless, eds., Amer. Math. Soc. 1997, pp. 239-250. Electronic version available at http: www.cecm.sfu.ca projects OMP . [PostScript] [PDF] [LaTeX] A condensed version, GUE eigenvalues and Riemann zeta function zeros: A non-linear equation for a new statistic has appeared in Phys. Rev. E 54 (1996), pp. R4493-R4495. [PostScript] [PDF] [LaTeX] Short proofs for nondivisibility of sparse polynomials under the extended Riemann hypothesis, D. Yu. Grigoriev, M. Karpinski, and A. M. Odlyzko, Fund. Inform. 28 (1996), pp. 297-301. Preliminary version on pp. 117-122 in Proc. Intern. Symp. Symbolic Algebraic Computation: ISSAC '92, P. S. Wang (ed.), ACM Press, (1992). [PostScript] [PDF] [LaTeX] Analytic computations in number theory, A. M. Odlyzko, Mathematics of Computation 1943-1993: A Half-Century of Computational Mathematics, W. Gautschi (ed.), Amer. Math. Soc., Proc. Symp. Appl. Math. 48 (1994), pp. 451-463. [PostScript] [PDF] [LaTeX] A New Lehmer pair of zeros and a new lower bound for the de Bruijn-Newman constant LAMBDA, G. Csordas, A. M. Odlyzko, W. Smith, and R. S. Varga, Electr. Trans. Num. Anal., 1 (1993), pp. 104-111. [PostScript] [PDF] [LaTeX] [comments] Nonexistence of Siegel zeros in towers of radical extensions, A. M. Odlyzko, and C. M. Skinner, pp. 499-511 in A Tribute to Emil Grosswald: Number Theory and Related Analysis, M. Knopp and M. Sheingorn (eds.), American Math. Soc., Contemporary Math. 143 (1993). [PostScript] [PDF] [LaTeX] Primes, quantum chaos, and computers, A. M. Odlyzko, pp. 35-46 in Number Theory, National Research Council (1990). [PostScript] [PDF] [TROFF] Bounds for discriminants and related estimates for class numbers, regulators, and zeros of zeta functions: A survey of recent results, A. M. Odlyzko, Sem. Theorie des Nombres, Bordeaux, 2 (1990), pp. 119-141. [PostScript] [PDF] [LaTeX] [PostScript of updated tables and references] [PDF of updated tables and references] [[LaTeX of updated tables and references] [comments] Supercomputers and the Riemann zeta function, A. M. Odlyzko, pp. 348-352 in Supercomputing '89: Supercomputing Structures Computations, Proc. 4-th Intern. Conf. on Supercomputing, L. P. Kartashev and S. I. Kartashev (eds.), Intern. Supercomputing Inst. (1989). [PostScript] [PDF] [TROFF] Fast algorithms for multiple evaluations of the Riemann zeta function, A. M. Odlyzko and A. Schoenhage, Trans. Am. Math. Soc., 309 (1988), pp. 797-809. [PostScript] [PDF] [TROFF] Large deviations of sums of independent random variables, H. L. Montgomery and A. M. Odlyzko, Acta Arith., 49 (1988), pp. 427-434. New analytic algorithms in number theory, A. M. Odlyzko, pp. 466-475 in Proceedings 1986 International Congress of Mathematicians, Amer. Math. Soc., 1987, [PostScript] [PDF] [TROFF] On the distribution of spacings between zeros of the zeta function, A. M. Odlyzko, Math. Comp., 48 (1987), pp. 273-308. [PostScript] [PDF] [TROFF] Computing pi(x): An analytic method, J. C. Lagarias and A. M. Odlyzko, J. Algorithms, 8 (1987), pp. 173-191. [PostScript] [PDF] [TROFF] Disproof of the Mertens conjecture, A. M. Odlyzko and H. J. J. te Riele, J. reine angew. Math., 357 (1985), pp. 138-160. [PostScript] [PDF] [TROFF] New algorithms for computing pi(x), J. C. Lagarias and A. M. Odlyzko, pp. 176-193 in Number Theory: New York 1982, D. V. Chudnovsky, G. V. Chudnovsky, H. Cohn and M. B. Nathanson (eds.), Springer-Verlag, Lecture Notes in Mathematics 1052, 1984. Gaps between zeros of the zeta function, H. L. Montgomery and A. M. Odlyzko, pp. 1079-1106 in Topics in Classical Number Theory: Coll. Math. Soc. Janos Bolyai 34., G. Halasz (ed.), North-Holland, 1984. On computing Artin L-functions in the critical strip, J. C. Lagarias and A. M. Odlyzko, Math. Comp., 33 (1979), pp. 1081-1095. A bound for the least prime ideal in the Chebotarev density theorem, J. C. Lagarias, H. L. Montgomery, and A. M. Odlyzko, Inventiones math., 54 (1979), pp. 271-296. On conductors and discriminants, A. M. Odlyzko, pp. 377-407 in Algebraic Number Fields, A. Frohlich (ed.), Academic Press, 1977. Lower bounds for discriminants of number fields II, A. M. Odlyzko, Tohoku Math. J., 29 (1977), pp. 209-216. Effective versions of the Chebotarev density theorem, J. C. Lagarias and A. M. Odlyzko, pp. 409-464 in Algebraic Number Fields, A. Frohlich (ed.), Academic Press, 1977. Lower bounds for discriminants of number fields, A. M. Odlyzko, Acta Arith., 29 (1976), pp. 275-297. Some analytic estimates of class numbers and discriminants, A. M. Odlyzko, Inventiones math., 29 (1975), pp. 275-286. Up [ Full publications list | Return to home page ]
The Music of the Primes
A popular article by Marcus du Sautoy on the Riemann Hypothesis; Science Spectra, Issue 11.
1.---When the British mathematician Andrew Wiles told the world about his proof of the Last Theorem of the seventeenth century French lawyer, Pierre de Fermat, it looked as if the Holy Grail had been grasped. Fermat's Last Theorem has often been called the greatest unsolved riddle of mathematics. But many mathematicians would argue that this name belongs rather to an idea first put forward in the middle of the nineteenth century by the German mathematician Bernhard Riemann: The Riemann Hypothesis. 2.---PRIME NUMBERS It remains unresolved but, if true, the Riemann Hypothesis will go to the heart of what makes so much of mathematics tick: the prime numbers. These indivisible numbers are the atoms of arithmetic. Every number can be built by multiplying prime numbers together. The primes have fascinated generations of mathematicians and non-mathematicians alike, yet their properties remain deeply mysterious. Whoever proves or disproves the Riemann Hypothesis will discover the key to many of their secrets and this is why it ranks above Fermat as the theorem for whose proof mathematicians would trade their soul with Mephistopheles. 3.---Although the Riemann Hypothesis has never quite caught on in the public imagination as Mathematics' Holy Grail, prime numbers themselves do periodically make headline news. The media love to report on the latest record for the biggest prime number so far discovered. In November 1996 the Great Internet Prime Search announced their discovery of the current record, a prime number with 378,632 digits. But for mathematicians, such news is of only passing interest. Over two thousand years ago Euclid proved that there will be infinitely many such news stories, for the primes never run dry. 4.---Rather mathematicians like to look for patterns, and the primes probably offer the ultimate challenge. When you look at a list of them stretching off to infinity, they look chaotic, like weeds growing through an expanse of grass representing all numbers. For centuries mathematicians have striven to find rhyme and reason amongst this jumble. Is their any music that we can hear in this random noise? Is there a fast way to spot that a particular number is prime? Once you have one prime, how much further must you count before you find the next one on the list? These are the sort of questions that have tantalized generations. 5.---Last year we celebrated the centenary of perhaps the deepest fact known to date about the prime numbers since Euclid. George Friedrich Bernard Riemann (1826-1866) Proved by the French mathematician Hadamard and the Belgian mathematician de la Vallee Poussin, the Prime Number Theorem tells us how many primes we should expect to find between 1 and any number N. For example in the first 100 numbers, it says that there should be 25 primes. But in the first million, only one in fifteen should be prime. It therefore gives the probability that a number will be a prime and iy further says that as the numbers get bigger this probability gets smaller. So the primes thin out, getting rarer and rarer. Euclid guarantees that there will always be more primes to find. On the other hand, the Prime Number Theorem tells you how rare they become. 6.---The theorem gives us a formula for how many primes we should expect to find less than any number N. But it is not an exact formula. And this inexactness is at the heart of the Riemann Hypothesis. There is an analogy here with coin tossing. If I toss a coin a million times, then with a fair coin we should get half heads and half tails. But we don't expect to get exactly five hundred thousand heads. By the nature of this being a random process we will not be surprised by a variation of about one thousand either side of this number. 7.---The Riemann Hypothesis would say that looking for primes is rather like tossing a coin. We have a one hundred year old formula which tells us roughly how many primes we should expect to find. But we know that this is not an exact formula. Riemann predicted that the error term in this formula is the same as the error we expect to see when tossing coins making the primes look in some sense like a random process. So given a prime, to find the next prime on the list will be like waiting for the next head to appear when tossing a coin. Given that we can't expect an exact formula, this distribution of the primes conjectured by Riemann is as nice a one as we could hope for. 8.---The Riemann Hypothesis says that there aren't any mysterious patterns that we haven't already discovered among the primes. If it were false it would imply that there was some structure in the primes that we had missed over the centuries. 9.---To prove his prediction, Riemann showed that you need to move the goal posts and prove a result in a seemingly unrelated area called complex function theory. These strange connections are one of the great themes of mathematics. Riemann identified a function which encoded the structure of the primes. A function is like a computer - you feed it a number and it outputs another number. In Riemann's function, called the Riemann zeta function, you actually feed in two numbers which define the co-ordinates of points on a flat piece of paper. We can therefore get a graphical representation of this function as a surface sitting above the piece of paper where the height of the surface above a point on the paper is the output of the function at that point. Figure 1 and 2 show two different pictures of this surface. (The picture should actually live in four dimensions but the output of the function has been doctored for our humble 3-D consumption.) 10.---It was Riemann's great insight that the behaviour of prime numbers, by their nature discrete objects where you have to jump from one to the next, should be connected with a smooth continuous surface like the zeta function. Nevertheless they are inextricably linked. 11.---One of the important features of a function are those numbers where the function outputs zero. These are like the harmonics of your function. For example, if one remembers the picture of the sin or cosine functions that one learns in school, the picture oscillates outputting zero at regular intervals. 12.---For Riemann's zeta function, these harmonics have an extra significance for they describe the sound of the primes.Therefore anything you can say about these harmonics should tell you significant things about the prime numbers. As we have drawn our picture the peaks actually represent the zeros or harmonics. You might notice that these first few peaks all seem to lie in a straight line. Riemann predicted that in fact all the points at which this function is zero should lie in a straight line where one of the co-ordinates is always 1 2. What is rather startling is that this very regimented behaviour of the harmonics implies the coin-tossing nature of the primes. This is in fact the conjecture that Riemann originally proposed and what mathematicians refer to as the Riemann Hypothesis: the zeros of the Riemann zeta function lie on a straight line. 13.---What evidence is there then for this conjecture being true? Riemann's papers show that he had quite sophisticated methods to detect zeros which led him to his conjecture. Unfortunately many of his writing were destroyed so it is unknown how much Riemann actually knew. Perhaps we might find his own marginal comment of a wonderful proof to rival Fermat's historic tease. The famous Cambridge mathematician G.H. Hardy in the twenties proved that infinitely many of these zeros lie in a line. He almost went on to provide the Riemann Hypothesis with a story to equal Fermat's cryptic note in the margin. On a rough sea crossing fearing for his life, he sent a joke telegram saying that he had found a wonderful proof of the Hypothesis. The ship, however did not sink. 14.---Since the arrival of the supercomputer it has been possible to test the conjecture way beyond Riemann's wildest dreams. It is now known that the first one and a half billion zeros lie on this straight line. However such convincing evidence can be misleading. At ATT Bell Labs Andrew Odlyzko together with Hermann te Riele proved that a related conjecture was in fact false despite similar overwhelming evidence. Since there are known to be infinitely many zeros, the computer will never be able to tell us conclusively that they all lie in a straight line. Instead we must rely on human insight for a solution, a relief perhaps to those unnerved by the victory of IBM's Deeper Blue over the chess Grand Master Gary Kasparov. 15.---It may seem surprising to find a commercial organisation like ATT interested in the Riemann Hypothesis. However prime numbers are no longer just the play thing of the mathematician but hold the key to the world's finances. The codes that protect our credit card numbers when we send them across the internet depend on mathematical puzzles about prime numbers which at present are too difficult for us or a computer to crack. However the insight that a proof of the Riemann Hypothesis would give us about the primes could be enough to make the secrets of today, tomorrow's public property. That is why you find the likes of ATT research laboratories dedicating time and money to monitoring progress in the ivory towers of academia.
Zhao, Liangyi
University of Toronto. Exponential sums, character sums, L-functions and automorphic forms. Publications.
Liangyi Zhao's Homepage
Zhan Tao
Shandong University. Additive theory of prime numbers; Exponential sums over prime variables; Bombieri-Vinogradov type mean value theoreoms; Riemann Zeta function and Dirichlet L-functions.
third Tao Zhan Address Shandong University Jinan, Shandong 250100 P.R. China Tel.: 86-531-8364972 Fax: 86-531-8565167 Email: zhantao @sdu.edu.cn Education B.S: Shandong University, 1983 M.S: Shandong University, 1985 Ph.D: Shandong University, 1987 Research Interests Additive theory of prime numbers Exponential sums over prime variables Bombieri-Vinogradov type mean value theoreoms Riemann Zeta function and Dirichlet L-functions Professional Positions 1989-1991, Associate Professor, Shandong University 1991-present, Professor, Shandong University 1991-1992, Research Fellow, University of Freiburg, Germany, supported by the Alexander von Humboldt Foundation Feb.-July 1996, Research Fellow, The University of Hong Kong, supported by the Croucher Foundation 1995-2000, Vice-President, Shandong University 2000-present, President, Shandong University; Chairman, Shandong Mathematics Society Publications [28] (with J.Y. Liu and M.C. Liu) Squares of primes and powers of 2. II, J. Number Theory 92 (2002), no. 1, 99-116. [27] (with J.Y. Liu) Distribution of integers that are sums of three squares of primes, Acta Arith. 98 (2001), no. 3, 207-228. [26] (with C. Bauer and M.C. Liu) On a sum of three prime squares, J. Number Theory 85 (2000), no. 2, 336-359. [25] (with J.Y. Liu) Hua's theorem on prime squares in short intervals, Acta Math. Sin. (Engl. Ser.) 16 (2000), no. 4, 669-690. [24] (with J.Y. Liu and M.C. Liu) Squares of primes and powers of $2$, Monatsh. Math. 128 (1999), no. 4, 283-313. [23] (with J.Y. Liu) Estimation of exponential sums over primes in short intervals. I, Monatsh. Math. 127 (1999), no. 1, 27-41. [22] (with J.Y. Liu) Sums of five almost equal prime squares. II, Sci. China Ser. A 41 (1998), no. 7, 710-722. [21] (with J.Y. Liu ) The Goldbach-Vinogradov theorem, Number theory in progress, Vol. 2 (Zakopane-Ko\'scielisko, 1997), 1005-1023, de Gruyter, Berlin, 1999. [20] (with J.Y. Liu ) On a theorem of Hua, Arch. Math. (Basel) 69 (1997), no. 5, 375-390. [19] (with M.C. Liu) The Goldbach problem with primes in arithmetic progressions, Analytic number theory (Kyoto, 1996), 227-251, London Math.Soc, Lecture Note Ser., 247, Cambridge Univ. Press, Cambridge, 1997. [18] (with J.Y. Liu ) The ternary Goldbach problem in arithmetic progressions, Acta Arith. 82 (1997), no. 3, 197-227. [17] (with J.Y. Liu) Exponential sums involving the M bius function, Indag. Math. (N.S.) 7 (1996), no. 2, 271-278. [16] (with J.Y. Liu ) A Bombieri-type mean-value theorem concerning exponential sums over primes, Chinese Sci. Bull. 41 (1996), no. 5, 363-366. [15] (with J.Y. Liu ) On sums of five almost equal prime squares, Acta Arith. 77 (1996), no. 4, 369-383. [14] (with D. Fischer) Some almost all results concerning the Pjateckii-Sapiro prime numbers, A Chinese summary appears in Chinese Ann. Math. Ser. A 17 (1996), no. 4, 515, Chinese Ann. Math. Ser. B 17 (1996), no. 3, 279-288. [13] (with J.Y. Liu ) A Bombieri-type mean value theorem for prime variable trigonometric sums, (Chinese) Kexue Tongbao (Chinese) 41 (1996), no. 3, 193-195. [12] (with J.Y. Liu ) Estimation of exponential sums over primes in short intervals. II, Analytic number theory, Vol. 2 (Allerton Park, IL, 1995), 571-606, Progr. Math., 39,Birkhuser Boston, Boston, MA, 1996. [11] (with J.F. Lin) Generalization of Bombieri's theorem and its applications, Sci. China Ser. A 38 (1995), no. 12, 1432-1443. [10] A generalization of the Goldbach-Vinogradov theorem, Acta Arith. 71 (1995), no. 2, 95-106. [9] (with D. Wolke) Some remarks on the binary Goldbach problem, Arch. Math. (Basel) 61 (1993), no. 3, 241-249. [8] (with D. Wolke) On the distribution of integers with a fixed number of prime factors, Math. Z. 213 (1993), no. 1, 133-144. [7] On the mean square of Dirichlet $L$-functions, A Chinese summary appears in Acta Math. Sinica 36 (1993), no. 3, 432, Acta Math. Sinica (N.S.) 8 (1992), no. 2, 204-224. [6] Davenport's theorem in short intervals, A Chinese summary appears in Chinese Ann. Math. Ser. A 12 (1991), no. 5, 644, Chinese Ann. Math.Ser. B 12 (1991), no. 4, 421-431. [5] On the representation of large odd integer as a sum of three almost equal primes, A Chinese summary appears in Acta Math. Sinica 35 (1992), no. 4, 575, Acta Math. Sinica (N.S.) 7 (1991), no. 3, 259-272. [4] Distribution of $k$-full integers, Sci. China Ser. A 32 (1989), no. 1, 20-37. [3] On the error function of the square-full integers, A Chinese summary appears in Chinese Ann. Math. Ser. A 10 (1989), no. 3, 388, Chinese Ann. Math. Ser. B 10 (1989), no. 2, 227-235. [2] Bombieri's thoerem in short intervals, A Chinese summary appears in Acta Math. Scinica 33 (1989), no. 2, 287, Acta Math. Sinica (N.S.) 5 (1989), no. 1, 37-47. [1] On a theorem of Darvenport [Davenport], Chinese Quart. J. Math. 2 (1987), no. 2, 52-58. Talks 1. The Goldbach-Vinogradov Theorem in Short Intervals, International Conference in Number Theory, Oberwohlfach 1991. 2. Some Remarks on the Binary Goldbach Problem, International Conference in Number Theory, Marseille, Luminy 1992. 3. On Integers with a Fixed Number of Prime Factors, Annual Meeting of the Germany Mathematics Society, Berlin 1992. 4. On the Distribution of a special Class of Integers, International Conference in Number Theory, Hong Kong 1993. 5. Estimation of Non-linear Exponential Sums over Primes, International Conference in Number Theory in Honor of Professor Heini Halberstam, Urbana-Champaign 1995. 6. The Goldbach Problem with Primes in Arithmetic Progressions, International Conference in Number Theory, Kyoto 1996. 7. On Some Problems in the Additive Prime Number Theory, Workshop and Conference in Number Theory, Hong Kong 1996. 8. On Sum of Prime Squares, International Conference in Number Theory in Honor of Professor Andrej Schinzel, Zakopane, Poland 1997. 9. The Goldbach-Vinogradov Theorem with Restrictions on Prime Variables, 101 Years of Prime Number Theorem, Ulm, Germany 1997.
Zimmermann, Paul
INRIA Lorraine. Computer algebra, the arithmetic of Big Numbers, random generation of combinatorial structures and reliable computation.
Paul Zimmermann's Home Page Paul Zimmermann ( recommandations to send me a document ) Publications and Code Here are some publications , talks , and some free tools I have written. I am interested in Computer Algebra (called Calcul Formel in French), in the arithmetic of Big Numbers , in the random generation of combinatorial structures and in reliable computations (actions FIABLE and AOC ). My preferred computer algebra systems are Maple and MuPAD . Here are some nice problems and their solutions. Here are some records concerning numbers. I work at INRIA ( some acronyms used here ) and LORIA in the Spaces project (I worked in the Polka project from 1997 to 2000 and previously in the Algo project in Paris. I am responsible of the axis "Algorithmics and Computer Algebra" of the GdR ALP . Other interesting links Table of Mathematical Constants , by Steven Finch Mathematical constants and computation by Xavier Gourdon and Pascal Sebah The Encyclopedia of Integer Sequences , by Neil Sloane Inverse Symbolic Calculator , from CECM Analysis of Algorithms Contact Information My address is: Paul Zimmermann, INRIA Lorraine, Technopole de Nancy-Brabois, 615 rue du Jardin Botanique, BP 101, F-54600 Villers-les-Nancy. My email is Paul(foo)Zimmermann(bar)loria(foo)fr, where (foo) should be replaced by a dot (.), and (bar) by the at-sign (@). Warning: my mail is automatically filtered by SpamAssassin, and any mail above the current cutoff will be rejected to dev null. My phone number is +33 (0)3 83 59 30 41, my fax is +33 (0)3 83 27 83 19 (dial the 0 only from France).
Zhu, Hui June
McMaster University. Arithmetic geometry.
Hui June Zhu's Buffalo homepage w e l c o m e WorldTime US-Clock Postal address: Hui June Zhu Department of Mathematics SUNY at Buffalo Buffalo , NY 14260 Phone: (716)-645-6284 Ext.131 Fax: (716)645-5039 email:hjzhu[at]math[dot]buffalo[dot]edu papers. .. seminars. .. courses... Below are Personal Links: Local-links: Lib , Academic Calendar , RSF , CampusMap city of Buffalo , weather , Toronto-region . More... search Cal - Lib Dic Languages. mathlinks morelinks , Mail? NYT
Zhang Shou-Wu
Columbia University. Arithmetic algebraic geometry.
Shou-Wu Zhang's HomePage Shou -Wu Zhang Professor of Mathematics Department of Mathematics Columbia University 2990 Broadway New York , NY 10027 , USA email: szhang@math.columbia.edu Office: 608 Mathematics Phone: (212)854-6362 Fax: (212)854-8962 Teaching (Fall, 2005) Topics in Arithmetic Algebraic Geom e try Tuesday and Thursday 10:35-11:50 am, Math 507 Ordinary Differential Equations Tuesday and Thursday 1:10-2:25 pm, Math 203 Office hours Tuesday 2:30-3:30 pm and Thursday 3:30-4:30 pm, Math 608 Seminars (Fall, 2005) Joint Number Theory Seminar Thursday, 5-7 pm, Columbia-CUNY-NYU Algebraic Geometry Seminar Friday , 2:30-3:30 , Math 520 Number theory arithmetic geometry workshop Monday, 1-3PM, Math 622 Preprints and Publications
Zhang Liang-Cheng
Southwest Missouri State University. Algebraic and analytic number theory.
Liang-Cheng Zhang 's Homepage Department of Mathematics Liang-Cheng Zhang Professor Education B.S. and M.S in Math, Peking(Beijing) University, China Ph. D. in Math, University of Illinois at Urbana-Champaign Research Interests - Algebraic and Analytic Number Theory Class Invariants and Singular Moduli Class Ideal Groups and Class Numbers of Quadratic Fields Unit Groups of Number Fields Class Field Theory, Genus Theory and Complex Multiplication Continued Fractions Elliptic Functions and Modular Forms q-Series Diophantine Equations Ramanujan's Work Selected Publications "Explicit evaluations of two Ramanujan-Selberg continued fractions" International Journal of Number Theory, to appear. "Explicit evaluation of a Ramanujan-Selberg continued fraction", Proceedings of AMS, 130, No. 1(2001), 9-14. "A certain quotient of eta-functions found in Ramanujan's Lost Notebooks, Pacific Journal of Mathematics,Vol. 202, No. 2 (2002), pp 267-304 (with Berndt, Chan and Kang). "Radicals and units in Ramanujan's work", Acta Arith., LXXXIL.4(1998), pp 145-158 (with Berndt and Chan). "Ramanujan's class invariants, Kronecker's limit formula and modular equations III", Acta Arith., LXXXII 4 (1997), pp 379-392. "Ramanujan's association with radicals in India", Amer. Math. Momthly, 104 (Dec., 1997), pp 905-911 (with Bruce Berndt and Chan). "Ramanujan's remarkable product of Theta functions", Proc. Edinburg Math. Soc., 40 (1997), pp 583-612 (with Berndt and Chan). "Ramanujan's class invariants, Kronecker's limit formula and modular equations", Trans. Amer. Soc., 349(1997), pp 2125-2173 (with Berndt Chan). "Ramanujan's class invariants with applications to the values of q-continued fractions and Theta functions", Fields Institute Communications, 14(1997), pp37-53 (with Berndt and Chan). "Ramanujan's class invariants, Kronecker's limit formula and modular equations II", Analytic Number Theory, Proceedings of Conference in Honor of H. Halberstam, Birhauser, (1996), Vol. 2, pp 817-838. "Explicit values of the Rogers-Ramanujan continued fractions", J.Reine Angew. Math., 480(1996), pp 141-159 (with Berndt and Chan). "Ramanujan's singular moduli", The Ramanujan Journal,1(1997), pp. 53-74 (with Berndt and Chan). "Ramanujan's class invariants and cubic continued fractions", Acta, Arith., 73(1995), pp 67-85, (with Berndt and Chan). "New criterion for class number one for real quadratic fields", Number Theory (CMS Conference Proceedings), Vol. 15, (1995), pp 245-248, (with R. Mollin). "A lower bound for the class number of a real quadratic field of ERD-type", Canadian Mathematical Bulletin, Vol. 37 (1994), pp 90-96, (with R. Mollin P.Kemp) "A new class of theta function identities originating in Ramanujan's Notebooks", Journal of Number Theory, Vol. 48, No. 2,(1994), pp 224-242, (with Berndt). "Ramanujan's continued farctions for products of Gamma functions", J. Math. Anal. and Appl., Vol. 174, No. 1, (1993), pp 22-52. "Orders in quadratic fields II", Proceedings of the Japan Academy, Vol. LXIX, Ser. A, No. 9, (1993), pp 368-371, (with R. Mollin). "Reduced ideals, the divisor function, continued fractions and class numbers of real quadratic fields", Publicationes Mathematicae, Debrecen, Tomus 43 3-4, (1993), pp 315-328, (with R. Mollin). "Ramanujan's identities for eta-functions", Mathematische Annalen, 292 (1992), pp 561-573, (with B. Berndt). "On unit solution of the equation xyz=x+y+z in total imaginary quartic fields", Journal of Number Theory, Vol. 40, No. 3 (1992), pp 255-263, (with H. Edgar and J. Gordon). "q-Difference equations and Ramanujan-Selberg continued fractions", Acta Arith., Vol. 57, No. 4, (1991) pp 307-355. "On unit solutions of the equation xyz=x+y+z in not total real cubic fields", Canadian Math. Bulletin, Vol. 34(1), (1991), pp 141-144, (with J. Gordon). "On unit solution of the equation xyz=x+y+z in a number field with unit group of rank one", Acta Arith., Vol. 57, No. 2, (1991), pp 155-158, (with J. Gordon). "Some q-integrals associated with modular forms", J. of Math. Anal. and Appl., Vol. 150, No. 1, (1990), pp 264-273. "On a diophantine equation of Modell in number theory", Acta Sci. of Sichuan Univ., (1990) pp 164-167. "On the units of cubic and bicubic fields", Acta Math. Sinica, New series, Vol. 1, No. 1, pp 22-34 (1985) "On a principle of reduction of fields Q(cubic root of m_1, ..., cubic root of m_r)", Advances in Math (Chinese), Vol. 12, No.3 (1983), PP 237-240. Favourite Activities Tennis , Table Tennis Watching NBA , NCAA , US Open Go (Weiqi) Reading and Music Travel Contact Information Email: liz917f@missouristate.edu Department of Mathematics Missouri State University Springfield, MO 65897 Phone: (417)836-5230 Some Interesting Links AMS(American Mathematical Society) CND(China News Digest) USA Today CNN Interative Fortune Interative Weather Information Network Liang-Cheng Zhang 2005 Back to the Math Department Page
Zuniga-Galindo, Wilson
Barry University. Algebraic geometry, number theory, p-adic analysis.
W Barry University W. A. Zuniga-Galindo Assistant Professor of Computer Science and Mathematics Office Address Department of Mathematics and Computer Science 11300 N.E. Second Avenue, Miami Shores, Florida 33161 Email Address wzuniga@mail.barry.edu Office Phone (305) 899-3616 SCHEDULE TEACHING PUBLICATIONS
Zaccagnini, Alessandro
University of Parma. Analytic Number Theory.
Alessandro Zaccagnini's Home Page Home General Research Papers Talks Teaching Personal Alessandro Zaccagnini's Home Page I am a member of the Department of Mathematics of the University of Parma , where I am Associate Professor since the end of 2004. I have been working there as Research Fellow since the end of 1992. My main research interest is in Analytic Number Theory, but I officially work in the field of Mathematical Analysis, since my subject is unknown to the Italian law which, believe it or not, does not recognize its existence (sic!). Introduzione alla crittografia di Alessandro Languasco e Alessandro Zaccagnini, Ulrico Hoepli Editore, ottobre 2004. Try the PURRS (Parma University Recurrence Relations Solver) online! Small gaps between primes exist! An account of the wonderful result by Goldston, Pintz and Yildirim. See also their full paper . Servizio orientamento Sono Responsabile per l'Area Matematica per l'Orientamento degli studenti delle Scuole Secondarie. Contattatemi ad uno degli indirizzi qui sotto per avere informazioni sui corsi di Matematica e di Matematica e Informatica. Per favore, NON scrivetemi per questioni relative ai piani di studio o simili, per le quali non sono competente. Mailing address Dipartimento di Matematica Telephone (+39) 0521 906902 Universit degli Studi di Parma (+39) 0521 906900 (operator) Parco Area delle Scienze, 53 a Telefax (+39) 0521 906950 Campus Universitario e-mail 43100 Parma, Italy Do not omit the leading zero when calling from abroad. Last updated on 15.11.2005: 09:03:08. Home General Research Papers Talks Teaching Personal Alessandro Zaccagnini 2005
Young, Matthew P.
American Institute of Mathematics. Arithmetic of elliptic curves. Publications.
Matthew P. Young Address: Matthew P. Young American Institute of Mathematics 360 Portage Ave. Palo Alto, CA 94306-2244 Electronic Mail Address: myoung@aimath.org Research Papers On the nonvanishing of elliptic curve L-functions at the central point (to appear in the Proceedings of the London Mathematical Society) dvi version postscript pdf Low-lying zeros of families of elliptic curves (To appear in JAMS) dvi version postscript pdf Older and longer version of Low-lying zeros of families of elliptic curves (with full details of torsion families and CM families) dvi version postscript pdf Lower order terms of the 1-level density of families of elliptic curves (Appeared in IMRN 2005, 10) dvi version postscript pdf Maintained by myoung@aimath.org and last modified 10 24 05
Yoshitomi, Kentaro
Kyoto University. Computational number theory. Elliptic curve and Jacobian arithmetic classes for LiDIA.
K Yoshitomi's Home Page Welcome to Kentaro Yoshitomi 's Web Page You are the th visitor. Now it is o'clock. Click Here for Japanese version. Profile (in Japanese) My programs Pages related to Computers (in Japanese) Link Collections (in Japanese) Back to Dept. of Math. Home Page yositomi@kusm.kyoto-u.ac.jp Ver 0.12 [Saturday, 06-Feb-1999 10:57:26 JST]
Yui, Noriko
Queen's University at Kingston, Ontario, Canada. Arithmetic algebraic geometry.
Noriko Yui Noriko Yui Ph.D., Rutgers Research group: Algebra and Number Theory E-mail address: yui@ny.mast.queensu.ca Research interests Arithmetic algebraic geometry
Yu, Jing
Academia Sinica, Taiwan. Number theory, Arithmetical algebraic geometry. Arithmetic of function fields, transcendence theory. Symbolic computation.
Jing Yu Jing Yu @@Jing Yu received a B.S. in Mathematics from National Taiwan Normal University. Afterwards he went to the United States and studied Mathematics at Yale University with Serge Lang. He went back to Taiwan immediately after receiving his Ph.D in 1980 and joined the Academia Sinica as an associated research fellow. In the year 1982 84 he traveled to France, as Boursier du gouvernement francais at Orsay (Universite de Paris-Sud). He was promoted to research fellow by the Academia Sinica in 1985. In the year 1987 88, he was a member of the Institute for Advanced Study at Princeton. He has also been a visiting member at the Max Planck Institut fur Mathematik in Germany. @@As a descendent of the Artin school, Jing Yu is interested in all phases of Number Theory and Arithmetical Algebraic Geometry. In recent years he has done major works in the arithmetic of function fields, especially transcendence theory. He is also interested in doing symbolic computations with computer. @@ Publications A Cuspidal class number formula for the modular curves X(N), Mathematische Annalen, 252(1980), 197-216. Irrationality of lattices in finite characteristic, Mathematika, 29(1982), 227-230. Transcendental numbers arising from Drinfeld modules, Mathematika, 30(1983), 61-66. Transcendence theory over function fields, Duke Mathematical Journal, 52(1985), 517-527. A six exponentials theorem in finite characteristic, Mathematische Annalen, 272(1985), 91-98. Transcendence and Drinfield modules, Inventiones mathematicae, 83(1986), 507-517. Transcendence and Drinfeld modules II, Proceeding of the summer research conference, NSC(1986), 172-181. Transcendence and Drinfeld modules: several variables, Duke Mathematical Journal, 58(1989), 559-575. On Periods and quasi-periods of Drinfeld modules, Compositio Mathematica, 74(1990), 235-245. Transcendence and special zeta values in characteristics p, Annals of Mathematics, 134(1991), 1-23. Transcendence in finite characteristics, The Arithmetic of Function Fields, ed. by D. Goss, D. R. Hayes and M. I. Rosen, de Gruyter, 1992. Analytic homomorphisms into Drinfeld modules, Annals of Mathematics 145(1997), 215-233. (With Jiu-Kang Yu) A note on a geometric analogue of the Ankeny-Artin Chowla conjecture, Contemporary Mathematics, AMS, 210 (1998), 101-105. On arithmetic of hyperelliptic curves, to appear in Aspects of Mathematics 1998. (With Julie T.-Y. Wang) On class number relations over function fields, Journal of Number Theory, (1997) (to appear). (With L.-C. Hsia) On singular moduli of Drinfeld modules in characteristic two, Journal of Number Theory, (1997) (to appear). (With C.-N. Hsu) On Artin's conjecture for rank one Drinfeld modules, (preprint 1997). (With L.-C. Hsia) On characteristic polynomials of geometric Frobenius associated to Drinfeld modules, preprint 1997. [ Chinese | Home | Research Staff ]
Yamamoto, Yoshihiko
Osaka University. Class groups, Construction of class fields, Fundamental units, Elliptic curves, Abelian varieties, Jacobians, Automorphic forms, Zeta functions.
My Home page Welcome to YAMAMOTO 's Home Page Japanese YAMAMOTO, Yoshihiko : Number Theory EClass Groups, Construction of Class Fields EFundamental Units EElliptic Curves, Abelian Vrieties, Jacobian Varieties EAutomorphic Functions, Automorphic Forms EZeta Functions Personal Data(in Japanese) Data for "A Course in Experimental Mathematics" (in Japanese) Class Numbers and Fundamental Units of Quadratic Fields Elliptic Curves over the Rationals Modular Curves Class Polynomials Under Construction Back to the Home Pages of Department of Mathematics, Faculty of Science, Osaka University Last modified: Apr 30, 1997
Young, Paul Thomas
College of Charleston. Sequences, L-functions.
Paul's Home Page Paul Thomas Young Welcome to my home page. I am a Professor on the faculty of the Department of Mathematics at the College of Charleston . If you don't believe me, just check my vita . Address Department of Mathematics College of Charleston 66 George Street Charleston, SC 29424-0001 USA phone: (843)953-5922 fax: (843)953-1410 paul@math.cofc.edu Classes Students in my Spring 2005 classes may access materials and information on WebCT . Happenings SERMON 2004 The Seventeenth SouthEastern Regional Meeting On Numbers was held at the College of Charleston April 16-18, 2004 Keynote Speaker: Harold M. Stark, UCSD Conference Webpage Meeting on Geometric Analysis and Singular Spaces Mathematisches Forschungsinstitut Oberwolfach June 2-8, 2002 Oberwolfach Web Site The Dwork Trimester in Italy "Remembering Bernie" A cycle of conferences on Dwork theory, in memory of Bernard M. Dwork May-July 2001 AMS Obituary Dwork Conference Web Site Preprints Here you can access preprints of some of my recent papers in pdf form. My earlier papers may also be found here . "On the behavior of some two-variable p-adic L-functions" , Journal of Number Theory 98.1 (2003), 67-88. "On lacunary recurrences" , The Fibonacci Quarterly 41.1 (2003), 41-47. "Congruences for degenerate number sequences" , Discrete Mathematics 270 (2003), 279-289. "Gauss sums and multinomial coefficients" , Journal of Number Theory 106.1 (2004), 13-25. "Degenerate and n-adic versions of Kummer's congruences for values of Bernoulli polynomials" , Discrete Mathematics 285 (2004), 289-296. "p-adic interpolation of the Fibonacci sequence via hypergeometric functions" (with Prerna Bihani and Wendy Sheppard), The Fibonacci Quarterly 43.3 (2005), 213-226. "Regular and strongly regular planar graphs" (with Nirmala Limaye, Dinesh Sarvate, and Pantelimon Stanica), Journal of Combinatorial Mathematics and Combinatorial Computing 54 (2005), 111-127. "On Lucas-Bernoulli numbers" , submitted to The Fibonacci Quarterly . Surf's Up! Catch some tasty waves to other way cool spots on the net. Check out the online version of Mathematical Reviews . Read gnarly preprints of recent articles in Algebraic Number Theory . Get way lost in Karl Dilcher's AMAZING Bernoulli Number Bibliography ! Scope out the rise and fall of the stock market .
Yildirim, Yalcin
Bogazii University. Small gaps between consecutive primes.
Cem Yaln Yldrm [ Back ] Cem Yaln Yldrm Bogazii University Faculty of Arts and Sciences Department of Mathematics Bebek 34342 Istanbul-TURKEY Phone: (0) 212 359 66 02 Fax: (0) 212 287 71 73
Yukie, Akihiko
Tohoku University. Geometric invariant theory, Zeta functions for prehomogeneous vector spaces, Applications to the Oppenheim conjecture.
Home page of Akihiko Yukie Japanese About myself Birthdate, Birthplace: Born on August 1, 1957 in Kofu Yamanashi Japan Kofu is a city about 80 miles west of Tokyo. The climate is similar to that of Oklahoma. It is surrounded by mountains and one of them is Mt. Fuji. Mt. Fuji is about 1 hour and half from Kofu Family: Married to Miho Yukie with two daughters Mayu (5 years old) and Tomomi (2 years old) Education: Ph. D. Harvard University 1986 BS University of Tokyo 1980 Employment: Professor Tohoku University 1999- Associate Professor OSU 1995-1999 Assistant Professor OSU 1989-1995 Guest Professor at SFB 170 Goettingen Germany 1990-1991 Member of Institute for Advanced Study Princeton 1989-1990 Visiting Assistant Professor OSU 1987-1989 Tamarkin Assistant Professor Brown University 1985-1987 Mathematical interest: Geometric Invariant Theory, Zeta functions for prehomogeneous vector spaces. Applications to the Oppenheim conjecture. Lectures on rational orbit decompositions of prehomogeneous vector spaces Anyone who wants the lecture note of my course on prehomogeneous vector spaces can copy its gzipped ps file course.ps.gz . Recent preprints The talk I gave in Kyoto The mean value theorem of the product of class numbers of paired quadratic fields I The mean value theorem of the product of class numbers of paired quadratic fields II Math Department Home Page
Ye, Yangbo
University of Iowa. Automorphic forms, Group representations, Automorphic L-functions, Relative trace formulae, Exponential sums, Distribution of primes.
Yangbo Ye, Ph.D. Yangbo Ye, Ph.D. Professor of Mathematics Professor of Radiology Affiliated Faculty of The Program in Applied Mathematical and Computational Sciences Affiliated Faculty of The Center for Asian and Pacific Studies The University of Iowa Li-Ching Chair Professor of Mathematics Shandong University Address Website for 22M:100, Summer 2005 Education Professional Positions Research in Number Theory Research in Computed Tomography Vita Yangbo Ye ( yey@math.uiowa.edu )
Yang, Tonghai
SUNY at Stony Brook. Number theory, representation theory, and arithmetic geometry: especially L-functions, Eisenstein series, theta series, Shimura varieties, intersection theory, and elliptic curves.
Tonghai Yang's homepage Tonghai Yang Welcome to my homepage which is still under construction. I am a assistant professor at the Department of Mathematics, SUNY at Stony Brook. I will be on leave to be an assistant professor at the University of Wisconsin at Madison during 2000-01. Address Department of Mathematics, SUNY at Stony Brook Stony Brook, NY 11794 Office Phone: (516)632-8267 Fax: (516)632-7631 Email: thyang@math.sunysb.edu Title: Assistant Professor Curriculum Vitae and Publications Click here to get a listing of my papers from the AMS MathSciNet with links to Mathematical Reviews. RESEARCH INTEREST My interest is in number theory, representation theory, and arithmetic geometry. I am especially interested in L-functions, Eisenstein series, theta series, Shimura varieties, intersection theory, and elliptic curves. Useful Links UofM Mathematics Department web site AMS Web site Number theory web Algebraic Number Theory Archives Representation theory preprints archive at University of Georgia Many math departments around the world, via Penn State. A useful list of addresses of math departments in Europe , and some links. Journals online HXWZ BLOOMBERG NEW YORK STOCK EXCHANGE New York Times Some Friends' Web Pages Stephen Miller Jeff Adams Ken Ono Jian-Shu Li Kevin Coombes Li Guo Chan Heng Huat Last Modified: Fri. Oct. 23 21:59:40 1998
Yu, Kunrui
Hong Kong University of Science and Technology. Transcendental number theory, diophantine approximation.
Kunrui YU's Home Page Kunrui YU (Dr. rer. nat., Bonn, 1987) Professor Research Interests: Transcendental number theory, diophantine approximations Email:makryu@uxmail.ust.hk Department of Mathematics Hong Kong University of Science and Technology Clear Water Bay, Kowloon Hong Kong
Xarles, Xavier
Universitat Autnoma de Barcelona. Abelian varieties over local fields.
Xavier Xarles Home Page Welcome to homepage Publications and talks Teaching Math links Mail addres: Departament de Matemtiques Universitat Autnoma de Barcelona E-08193 Bellaterra (Barcelona) Catalunya, SPAIN Office phone number: (34)-3-581-4379 Fax: (34)-3-581-2790 xarles@mat.uab.es
Wan, Daqing
University of California Irvine. Number theory and arithmetic geometry. Publications, preprints.
Daqing Wan's homepage Daqing Wan Professor of Mathematics University of California Irvine, CA 92697-3875 Office: MST 279 Tel: (949) 824-7013 Fax: (949) 824-7993 Email: dwan@math.uci.edu Research Interests : Number Theory and Arithmetic Geometry Curriculum Vitae ps pdf Papers and Preprints Teaching Fall 2002-Spring 2003: Algebra 230A-B-C, Abstract Algebra 120 Fall 2003-Spring 2004: Algebraic Number Theory 232A-B-C, Topics in Algebra 234 Fall 2004: Math 2A (Calculus) 2A, Sections E and F Spring 2005: Math 234 (Topics in Algebra). Fall 2005: Algebraic Number Theory 232A, Linear Algebra 121B Seminar Number Theory Seminar Last modified on September 22, 2005.
Watkins, Mark
University of Bristol. Arithmetic of elliptic curves; special values of higher symmetric power L-functions. Publications.
Mark Watkins Mark Watkins Papers Page Curriculum Vitae Research Projects: 1. Experiment on the lattice distribution of rank 2 elliptic curves with prime conductor. In joint work with William Stein, I have created an enormously large database of elliptic curves. Using the recent work of Tom Womack on 4-descent, I plan to investigate the lattice distribution for the 2.1 million rank 2 curves with prime conductor. The recent work of Cremona, Prickett, and Siksek on saturation will also be used to certify that a Mordell-Weil basis has been found. Another data set to be investigated is that of rank 2 elliptic curves with absolute discriminant less than 100 million. This will hopefully be done in time for ANTS VII. 2. Special values of higher symmetric power L-functions of elliptic curves. Conjectures of Deligne and Bloch-Kato suggest that symmetric power L-function of elliptic curves should satisfy functional equations, and the special values they take should have arithmetic significance. My work on the modular degree can be seen as a large experiment regarding the symmetric square. Buhler, Schoen, and Top have done a similar investigation for the symmetric cube. Christophe Delaunay, Neil Dummigan, Phil Martin, and I plan to investigate higher symmetric powers. In particular, Martin has determined the proper Euler factor for symmetric powers at additive primes, and Delaunay has generic PARI code to compute special values. E-mail: watkins@math.psu.edu
Walsh, Gary
University of Ottawa. Diophantine analysis. Publications and links.
Gary Walsh's homepage Gary Walsh Where I Am Adjunct Professor of Mathematics in the Department of Mathematics and Statistics at the University of Ottawa, Ottawa, Ontario, Canada. Snail Mail Address: Gary Walsh Dept. Math. University of Ottawa 585 King Edward St. Ottawa, Ontario, Canada K1N-6N5 Who I Am After receiving my Ph.D. under the supervision of Professor Cameron L. Stewart at The University of Waterloo , I held an NSERC (Canada) Postdoctoral Fellowship in the Department of Mathematics at the University of Ottawa from 1994 to 1996, and now an Adjunct Professor in the Department of Mathematics at the University of Ottawa doing research in Number Theory, specifically Diophantine Analysis. Publications etc. How to Reach Me gwalsh@mathstat.uottawa.ca Math Links The Canadian Number Theory Association The Number Theory Web The Canadian Mathematical Society The American Mathematical Society The Fields Institute A Listing of Journals Online Elliptic Curve Webpage DIOPHANTINE NET (France) Other Links National Hockey League The PGA Tour Gary's Golf Pictures (under construction) geovisit();
Weng, Annegret
Johannes Gutenberg-Universitt, Mainz. Arithmetic of elliptic curves. Publications. English German.
Meine Hompage
Wittmann, Christian
cole Polytechnique Fdrale de Lausanne. Algebraic Number Theory with a focus on explicit and computational methods. Publications, tables of cyclic cubic fields.
Homepage Christian Wittmann Dr. Christian Wittmann Address Universitt der Bundeswehr Mnchen Fakultt fr Informatik Institut fr Theoretische Informatik und Mathematik 85577 Neubiberg Germany My office: Building 41 400, Office 1413 Phone: +49 89 60043387 Fax: +49 89 60042876 E-mail: wittmann@informatik.unibw-muenchen.de Short CV Research interests Publications and Preprints Teaching (in German) Links last modified: June 22, 2005
Wingberg, Kay
Universitt Heidelberg. Algebraic number theory, Iwasawa theory; arithmetic geometry; structure of profinite (or pro-p) groups. Publications.
Prof. Dr. Kay Wingberg Universitt Heidelberg Mathematisches Institut Im Neuenheimer Feld 288 D-69120 Heidelberg Germany Telefon: +49-(0)6221-54-4897, Sekretariat: -5766, Telefax: -8312 Email: wingberg@mathi.uni-heidelberg.de Sprechstunde: Donnerstags 10-11 Uhr Zi. 226 INF 288 Research interests Publikationen Research interests Algebraic Number Theory, Iwasawa Theory, Arithmetic Geometry, Structure of profinite (or pro-p) Groups Publikationen Cohomology of Number Fields (with Jrgen Neukirch and Alexander Schmidt) 1. p-Potenzen und Kommutatoren in Verzweigungsgruppen p-adischer Zahlkrper 2. Die Einsheitengruppe von p-Erweiterungen regulrer p-adischer Zahlkrper als Galoismodul 3. Die p-Vervollstndigung der multiplikativen Gruppe einer p-Erweiterung eines irregulren p-adischen Zahlkrpers (with Uwe Jannsen) 4. Einbettungsprobleme und Galoisstruktur lokaler Krper (with Uwe Jannsen) 5. Existenz unendlicher algebraischer Zahlkrper, ber denen jedes Einbettungsproblem lsbar ist 6. Eine Bemerkung zum Einbettungsproblem mit nicht-abelschem Kern 7. Die Struktur der absoluten Galoisgruppe p-adischer Zahlkrper (with Uwe Jannsen) 8. Der Eindeutigkeitssatz fr Demuskin-Formationen 9. Demuskin-Erzeugende einer elementar-abelschen p-Erweiterung (with Uwe Jannsen) 10. Freie Produktzerlegungen von Galoisgruppen und Iwasawa- Invarianten fr p-Erweiterungen von Q 11. Ein Analogon zur Fundamentalgruppe einer Riemann'schen Flche im Zahlkrperfall 12. Duality theorems for -extensions of algebraic number fields 13. Positiv-zerlegte p-Erweiterungen algebraischer Zahlkrper 14. -berlagerungen von P1\{p1,p2,p3} 15. Galois groups of number fields generated by torsion points of elliptic curves 16. Artin Verdier duality for n-dimensional local fields involving higher algebraic K-sheaves (with Christopher Deninger) 17. On Poincar groups 18. On the product formula in Galois groups 19. On the rational points of abelian varieties over Zp-extensions of number fields 20. On the Beilinson-conjectures for elliptic curves with complex multiplication (with Christopher Deninger) 21. A Riemann-Hurwitz formula for the Selmer group of an elliptic curve with complex multiplication 22. Representations of locally profinite Groups 23. Duality Theorems for abelian varieties over Zp-extensions 24. Galois groups of Poincar type over algebraic number fields 25. On Demuskin groups with involution 26. On Galois groups of p-closed number fields with restricted ramification 27. On the etale K-theory of elliptic curves with complex multiplication for regular primes 28. On a Galois extension with restricted ramification related to the Selmer group of an ellipitic curve with complex multiplication 29. On Galois groups of p-closed number fields with restricted ramification II 30. On the fundamental group of a smooth arithmetic surface (with Alexander Schmidt) 31. On the maximal unramified p-extension of an algebraic number field 32. On positively ramified extensions of algebraic number fields 33. Safarevic's theorem on solvable groups as Galois group (with Alexander Schmidt) 34. Galois groups of local and global type 35. On the Fontaine-Mazur Conjecture for CM-Fields 36. Free Product Decomposition of Galois Groups of Number Fields 37. On ebotarev sets 38. Free quotients of Demuskin groups with operators 39. Free pro-p extensions of number fields
Wang Wei
Shandong University. Distribution of primes; the Riemann zeta function and Dirichlet L-functions.
third Wei Wang Address School of Mathematics System Science Shandong University Jinan, Shandong 250100 P.R. China Tel.: 86-531-8906961 Fax: 86-531-8902167 Email: wangwei@cfgauss.uni-math.gwdg.de Education B.S: Shandong University, 1982 M.S: Shandong University, 1984 Ph.D: Shandong University, 1987 Research Interests Distribution of Primes Riemann Zeta Function and Dirichlet L-function Overseas Research Experience 1988-1990, Institute of Mathematics, Oxford Univesity in UK, Post-Doctoral 1996-1997, Department of Mathematics, University of Goettingen in Germany Department of Mathematics, University of Freiburg in Germany Supported by the German Academic Exchange Center (DAAD) Publications [6] Inversion formula of Dirichlet polynomials and the approximate functional equation of Dirichlet's $L$-functions, Arch. Math. (Basel) 69 (1997), no. 4, 305-312. [5] On the approximate functional equation of Dirichlet $L$-functions, Quart. J. Math. Oxford Ser. (2) 48 (1997), no. 189, 127-132. [4] Estimating exponential integrals with a smooth weight function, Sci. China Ser. A 37 (1994), no. 9, 1041-1046. [3] On the least prime in an arithmetic progression, A Chinese summary appears in Acta Math. Sinica 35 (1992), no. 4, 575, Acta Math. Sinica (N.S.) 7(1991), no. 3, 79-289. [2] Fourth power mean value of Dirichlet's $L$-functions, International Symposium in Memory of Hua Loo Keng, Vol. I (Beijing, 1988), 293-321, Springer,Berlin, 1991. [1] On the least prime in an arithmetic progression, (Chinese) Acta Math. Sinica 29 (1986), no. 6, 826-836.
Wool, Assaf
Compugen. Groups, fundamental domains, Hecke operators, number fields. Software for modular curves and Shimura curves.
Assaf Wool's Home Page Assaf Wool's Home Page Contents Family Photos Math Projects Contact Information Favorite Links Biographical Information Personal Interests Math Projects Fundamental domains for subgroups of SL2(Z) - for G0(N) and G1(N), including free generators for these groups. Mobius transformations - definition and simple facts. Modular quaternion groups - GAP program that finds generators and fundamental regions for the unit group in a maximal order of a Rational quaternion algebra. Back to top Contact Information email address: assafwool@yahoo.com Back to top Favorite Links MathNerds - a great place to ask questions in all topics of mathematics, and if you're lucky you might get an answer from me. J.S. Milne's math page - a great place to learn about number theory. Thank you Prof. Milne. Sky Telescope - for all things astronomical. finance.yahoo - keeping in touch with the New York stock market. Walla news - news in Israel. NBA - best basketball in the world. ATP tour - latest in men's tennis. Back to top Biographical Information I am currently working in Compugen as an algorithm designer. Previously I worked as a teaching assistant in the Hebrew University in Jerusalem, studying for a Ph.D. in mathematics which I haven't completed. My wife Irit is a social worker, working with the mentally disabled. Back to top Personal Interests I am interested in mathematics, especially algebra and number theory (groups, fundamental domains, Hecke operators, number fields). I enjoy singing in a choir, hiking and walking, and watching the stars when the sky is dark and clear. Back to top Last Revised: 10 11 2004 geovisit();
Wewers, Stefan
University of Bonn, Germany. Arithmetic geometry. Publications and preprints.
Stefan Wewers Mathematisches Institut Stefan Wewers wissenschaftlicher Mitarbeiter am Mathematischen Institut der Rheinischen Friedrich-Wilhelms-Universitt Bonn Adresse: Beringstrae 1, 53115 Bonn, Germany E-mail: wewers mit der fr die Mathematik Bonn blichen Adresse: @math.uni-bonn.de Bro: Beringstrae 6, Zimmer 26 Telefon: +49-(228)-73-7641 Sprechstunde: Montags 16-17 Uhr, und nach Vereinbarung Arbeitsgebiet Arithmetische Geometrie Publikationen Variation of local systems and parabolic cohomology , with Michael Dettweiler, to appear in: Israel J. Math. Alternating groups as monodromy groups in positive characteristic, with Irene Bouw, to appear in: Pacific. J. Math. Formal deformation of curves with group scheme action , to appear in: Annales de l'Institut Fourier Reduction of covers and Hurwitz spaces , with Irene Bouw, J. Reine Angew. Math. (Crelle J.) 574 (2004) Stable reduction of modular curves, with Irene Bouw, in: Modular curves and abelian varieties, Progress in Math., Birkhaeuser, 2004 Three point covers with bad reduction, J. Amer. Math. Soc. 16 (2003), no. 4, 991-1032 Reduction and lifting of special metacyclic covers, Ann. Sci. Ecole Norm. Sup. (4) 36 (2003), no. 1, 113-138 Field of moduli and field of definition of Galois covers, in: Arithmetic fundamental groups and noncommutative algebra, 221-245, Proc. Sympos. Pure Math., 70, AMS, 2002 Deformation of tame admissible covers of curves , in: Aspects of Galois theory, 239-282, London Math. Soc. Lecture Note Ser., 256, Cambridge Univ. Press, 1999 Preprints Variation of parabolic cohomology and Poincare duality, with Michael Dettweiler, math.AG 0411119 The local lifting problem for dihedral groups, with Irene Bouw, math.AG 0409395 Hurwitz spaces, with Matthieu Romagny, notes for our talks at Luminy, march 8.-12. Canonical and quasicanonical lifts, Stable reduction of three point covers , Summary of my talk at the Journes Arithmetiques 2003 in Graz, math.AG 0401024 Construction of Hurwitz spaces , PhD-Thesis, Essen, 1998 Konferenzen Galois Theory and Arithmetic (GATA) , 1.-4. Juni, Bonn Aktuelle Lehrveranstaltung WS 2003 2004 Elementare Zahlentheorie
Wolff, Alison
University of Adelaide. Contact information.
Dr Alison Wolff Dr Alison Wolff Senior Lecturer Room: Mathematics Building 212 Phone: (08) 8303 3245 Fax: (08) 8303 3696 Email: awolff@maths.adelaide.edu.au Back to the Pure Mathematics homepage
de Weger, Benne
Eindhoven University of Technology. Diophantine problems, ABC conjecture.
Benne de Weger
Wu, Hsin-Tai (Eric)
Automorphic forms, representations, Hilbert modular forms of half integral weight, p-adic interpolation. Software, thesis (PDF).
Index Page Index Page | My Photo Album | File Sharing Home Page of Eric Wu Computer and programming Files to share Academic research My Photo Album Teaching Thinking and Learning
Weingartner, Andreas
Southern Utah University. Contact information.
SUU - Andreas J. Weingartner SUU Home | A-Z Index | Contact Info | Search Andreas J. Weingartner Assistant Professor of Mathematics Phone: 435-865-8611 Fax: 435-865-8666 Office: SC 212 E-Mail: weingartner@suu.edu - Course Information - Actuarial Science Emphasis - Professional Information - Department of Mathematics - SUU Faculty Listing Last Update: Thursday, March 10, 2005 Southern Utah University - 351 West University Boulevard - Cedar City, UT 84720 - 435.586.7700 2005 Southern Utah University | Disclaimer Note: This site is accessible to any browser, although, it will look much better in a browser that supports web standards. To view this page properly, please upgrade your browser. We recommend: Mozilla Firefox (download) Netscape Navigator 7.2 (download)
Wagner, Marcus
Technische Universitt Berlin. Algebraic number theory.
Marcus Wagner Marcus Wagner Address: Technische Universitt Berlin FB 3 - Mathematik MA 8-1 Strae des 17. Juni 136 D-10623 Berlin Germany phone: 030 314-23761 (MA 812) email: wagner@math.tu-berlin.de Research Interests: Algebraic number and function fields Publications On the computation of Hermite-Humbert constants for real quadratic number fields (preprint) [ PS , PDF ] Table of Humbert forms This table contains 19 Humbert forms which are listed with their minimal vectors, eutactic coefficients and the dimension of perfection. 16 Humbert forms are extreme. [ PS , PDF ] TU-Berlin | Mathematics Department | KANT Last modified: 2005-07-18 16:40
Wamelen, Paul van
Louisiana State University. Genus 2 curves, class number formulae, Jacobi sums, Stark's conjectures, computational projects.
Paul B. van Wamelen Paul B. van Wamelen Associate Professor Education Undergraduate: University of South Africa in Pretoria , 1985, University of Pretoria 1986-1988. Graduate: University of California, San Diego 1989-1994. Professional Experience Associate Professor, Louisiana State University , Aug 2001-present. Spent the 2002 2003 academic year at the University of Sydney working on the Magma computational algebra system . Assistant Professor, Louisiana State University , 1994-Jul 2001. Spent the calendar year 1997 at University of South Africa . Research My main research interest is Number Theory. My thesis and some subsequent work dealt with genus 2 curves. I've done some work on class number formulas, Jacobi sums, and recently, some computational work on Stark's conjectures. Currently I'm working on various computational projects. The Stark's conjecture paper has not been published yet, but for now a question: Can you see a pattern (any pattern!) in this picture ? If you can let me know and we might be famous... Publications For a full list of publications look here . Data The following are data sets that I have computed. Some of this did not fit in the various articles and are only published here. Genus 2 CM curves defined over the rationals Isogenies for Smart's curves Motzkin-Rabin geometries Programs Some of the programs used to compute the above data might be of interest to other researchers interested in computations on genus 2 curves and their Jacobians. They can now be found at this page. Anyone interested in the Somos 6 sequence should look at the worked example. Other You can play the board game Hex online You can play all kinds of lesser known board games with other enthusiast on Richard's PBeM server (by e-mail). Some games have a graphical interface. You can see games in progress here and here . Department of Mathematics Louisiana State University Baton Rouge, LA, 70803-4918 Office: 208 Lockett Phone: (225) 578-1675 Fax: (225) 578-4276 Email: wamelen@math.lsu.edu Created: March 18, 1998. Last modified: Aug 16, 2005. http: math.lsu.edu ~wamelen index.html
Weiss, Alfred
University of Alberta. Group representations and number theory.
Alfred Weiss . Alfred Weiss Professor Ph.D., Ohio State Office: CAB 531 Phone: (780) 492-3420 Fax: (780) 492-6826 Email: Research Interests Group representations and number theory. There are many natural Galois actions in algebraic number theory. The goal is to develop methods which are adquate for their description and also amenable to being studied arithmetically. CV Department of Mathematical and Statistical Sciences University of Alberta 632 Central Academic Building Edmonton, AB T6G 2G1 Phone: 780.492.3396 Fax: 780.492.6826 Last modified 11.22.04 | Home | U of A | Faculty of Science | Privacy Statement | | Site Map |
Wakabayashi, Isao
Seikei University, Tokyo. Diophantine equations and transcendence problems for values of analytic functions.
Wakabayashi's Home Page
Weintraub, Sol
Queen's College, New York. Number theory, statistics and probability.
Sol Weintraub Sol Weintraub saw@forbin.qc.edu Kiely 411997-5816 Highest Degree Ph.D., Temple University Specialty Number Theory, Statistics and Probability
Wagstaff, Samuel S. Jr
Purdue University. Cryptography, parallel computation, and analysis of algorithms, especially number theoretic algorithms. Publications, updates on the Cunningham project, software.
Department of Computer Science: Faculty: Samuel S. Wagstaff, Jr. Purdue Home Purdue Search Purdue Visit Giving College of Science Computer Science Faculty Computer Science Portal Purdue Login Password Search CS via Google Science Portals For Prospective Students For Current Students For Alumni and Friends For Faculty Staff Computer Science About Us People Faculty Visitors Staff Graduate Students Student Organizations Academic Programs Research News Calendar External Relations Resources Department of Computer Sciences 250 N. University Street West Lafayette, IN 47907-2066 Phone: (765) 494-6010 Send E-Mail Visit Homepage Samuel S. Wagstaff, Jr. Professor of Computer Science (1983) Education: BS, 1966 Massachusetts Institute of Technology PhD, 1970 Cornell University Before coming to Purdue, Professor Wagstaff taught at the Universities of Rochester, Illinois, and Georgia. He spent a year at the Institute for Advanced Study in Princeton. His research interests are in the areas of cryptography, parallel computation, and analysis of algorithms, especially number theoretic algorithms. He and J. W. Smith of the University of Georgia have built a special processor with parallel capability for factoring large integers. He is the author of Factorizations of bn 1 1, b = 2, 3, 5, 6, 7, 10, 11, 12 up to high powers, Contemporary Mathematics series, v. 22, Third edition, American Mathematical Society, 2002 (with John Brillhart, D. H. Lehmer, J. L. Selfridge and Bryant Tuckerman) (See http: www.ams.org online_bks conm22 ) and Cryptanalysis of Number Theoretic Ciphers, CRC Press, 2002. Selected Publications Samuel S. Wagstaff, "Prime numbers with a fixed number of one bits or zero bits in their binary representation", Experimental Mathematics, Volume 10 (2001), pp. 267-273. Samuel S. Wagstaff, "Prime divisors of the Bernoulli and Euler numbers", Proceedings of the Millennial Conference on Number Theory, Urbana, Illinois, May 21-26, 2000, M. A. Bennett, B. C. Berndt, N. Boston, H. G. Diamond, A. J. Hildebrand, W. Philipp, eds. B. Dodson, A. K. Lenstra, P. Leyland, A. Muffett, and Samuel S. Wagstaff, "MPQS with three large primes", Proceedings of the Algorithmic Number Theory Symposium 2002, Volume 2369 of Springer-Verlag Lecture Notes in Computer Science, pp. 448-462, 2002.
Wright, David
Oklahoma State University. Algebraic number theory and algebraic groups, with methods from functional analysis and analytic number theory.
HOME PAGE OF DAVID J. WRIGHT David J. Wright's Home Hello: I am a mathematician on the faculty of Oklahoma State University. My home page is divided up into the following areas of information: Current Teaching Schedule My resume and other personal information Some facts about my education, career and family are given here. Guide to my published works. MSRI MathGraphics info: notes and info about lectures Number Theory and PARI This a web supplement I created to the textbook Elementary Number Theory and its Applications by Ken Rosen. It contains among other things: Web tools for Number Theory Web tools for Cryptology Student Projects in Number Theory and Cryptology The Indra's Pearls Web Site Information on a book about kleinian groups which I co-authored and which is now published by Cambridge University Press. MATH 6490: Indra's Pearls Course Materials The course ran in the spring of 2004. Introduction to Dynamical Systems and Fractals These are the materials I prepared for a course given in the spring of 1996, including a 170-page book processed in latex2html. Symmetry Web This is a World Wide Web machine for experimenting with symmetry groups of simple geometric figures. The Putnam Competition Here is information about participating in the Putnam Competition, a national undergraduate math contest. Links to the World Wide Web This is my own personal collection of useful web links. This is continuously updated and out-of-date. The Oklahoma State University Mathematics Department's Home Page Interests Number Theory Observations of N. Katz in 1994-1995 on the finer distribution of Gauss sum angles and similar objects (Many results are now published by Katz and Sarnak.) Computations in regard to the above observations A Discussion of the RSA-129 Activity Kleinian Groups Discussion of Limit Sets Last modified: Wed Oct 19 17:20:51 BST 2005
Wooley, Trevor
University of Michigan. Analytic number theory: the Hardy-Littlewood circle method.
Trevor Wooley's homepage Trevor Wooley Office Phone: 734-936-1765 Address: Department of Mathematics, University of Michigan, 2074 East Hall, 530 Church Street, Ann Arbor, MI 48109-1043 Title: Professor NEWS FLASH 1st August 2005: I have escaped from 3 years of being Department Chair, so --- as they say --- normal service will be resumed shortly Click Curriculum Vitae here to look at a copy of my CV. Click Publication list here to see a list of my recent publications. This is a link to my research profile (to learn about some of my more recent interests, look here or here ). Personal Description: Welcome to the University of Michigan, home of the Hardy - Littlewood method (and more analytic number theory besides). Interested in number theory at the University of Michigan ? Why not come see us! We have students, postdoctoral workers, and visitors funded both through the NSF, and a Fellowship from the David and Lucile Packard Foundation. Here's a list of my students: Morley Davidson (PhD 1995, University of Georgia, Athens, 1997: Kent State University, Ohio, 1996- ;Institute for Advanced Study, 1995-96) Greg Martin (PhD 1997, Institute for Advanced Study, 1997-98; University of Toronto, 1998-2001) Joel Wisdom (PhD 1998, U.S. Government) Eric Freeman (PhD 1999, NSF Postdoc to University of Colorado, Boulder, 1999-2001; Institute for Advanced Study, 2001-02;) Scott Parsell (PhD 1999, Texas AM, 1999-2001; NSF Postdoc to Pennsylvania State University, 2001-4;) Mike Knapp (PhD 2000, Rochester, 2000-2003); Matthew Smith (PhD 200?); Craig Spencer (PhD 200?); Watch this space for newcomers! Recent and upcoming graduate courses: 567 Introduction to Coding Theory (Winter 2000, Winter 2001); 575 Introduction to Number Theory (Winter 1992, Fall 1998, Fall 1999, Fall 2000); 675 Introduction to Analytic Number Theory (Fall 1993); 677 Introduction to Diophantine Problems (Fall 2000); 775 The Hardy-Littlewood Method (Fall 1992, Fall 1996); 777 Local Solubility Problems for Forms in Many Variables (Fall 1995); 777 Diophantine problems in Many Variables (Winter 1999); [258x (at Harvard) Analytic methods for diophantine problems (Fall 2001)] NOTE 1: MATH DEPARTMENT EMAIL ADDRESSES HAVE ALL CHANGED!!! IF YOU SEND EMAIL TO THE OLD MATH.LSA.UMICH.EDU ADDRESS, IT IS GOING INTO AN ELECTRONIC BLACK-HOLE. THANKS TO THE WISDOM OF PEOPLE WHO SHOULD KNOW BETTER, WE NOW USE UMICH.EDU ADDRESSES AND NOTHING ELSE WORKS --- AND WE CANNOT DETECT WHEN MAIL IS SENT TO THE FORMER ADDRESS. NOTE 2: MATH DEPARTMENT PHYSICAL ADDRESS HAS CHANGED, THOUGH WE HAVE NOT MOVED!! See above, and see NOTE 1 for comments on this! wooley@umich.edu .
Woodcock, Chris
University of Kent at Canterbury. Commutative algebra, algebraic geometry and algebraic number theory; p-adic analogues of classical functions and their applications in number theory.
IMSAS Staff - Dr Chris Woodcock, University of Kent Skip search Search: all of kent.ac.uk IMSAS only text only University of Kent Dr Chris Woodcock You are here: Kent home ims people cfw Senior Lecturer in Pure Mathematics Pure Mathematics Group Publications Room: E221 Telephone internal 3803 external +44 1227 823803 Email C.F.Woodcock@kent.ac.uk Interests: Commutative algebra, algebraic geometry and algebraic number theory; p-adic analogues of classical functions and their applications in number theory. contact us at ims_secs@kent.ac.uk - University of Kent, 10 December 2004 Skip browse form Browse: Main website sections About the University Maps and directions Courses and studying at Kent Research Services for business Schools and colleges Arts, leisure and public events Conference, functions and holidays Departments and people Alumni, families and friends Student and staff intranet News, press releases and job vacancies
Wong, Siman
University of Massachusetts. Automorphic forms and Galois representations.
Siman Wong, Assistant Professor Siman Wong Assistant Professor Mailing Address: Department of Mathematics Statistics Lederle Graduate Research Tower, Box 34515 University of Massachusetts Amherst, MA 01003-4515 USA Office: LGRT 1119 Phone: 545-0907 Fax: 413-545-1801 E-mail: siman@math.umass.edu Visit Siman Wong's Personal Home Page . Back To "Faculty, Emeritus Appointments and Lecturers "
Wolf, Marek
Uniwersytet Wroclawski. Theoretical physics; distribution of primes.
Marek Wolf's home page Marek Wolf "... upon looking at prime numbers one has the feeling of being in the presence of one of the inexplicable secrets of creation." D.Zagier in Math. Intellig. 0 (1977), p.8, left column I am a theoretical physicist at the Institute of Theoretical Physics . In the late seventies I started working on strings and supersymmetry. This was my major field of interest until 1984, when I bought the famous ZX Spectrum computer (for less than 200$ !!!). Only then did I understand what good physics was. Immediately I turned from quantum field theory to fractals and chaos. Since Summer 1995 I am also interested in prime numbers, but I still believe that: Physics is Fun ! Curriculum vitae (look also here ) List of publications My favorite web sites e-mail: can be found here tel. (48 71) 3759-473, Below you can find my papers on the prime numbers: This figure presents the main results reported in the paper: Some Conjectures on the Gaps between Consecutive Primes (1.4 MB) Here is gzip-ed file: Download "conjectures.ps.gz" (420 kB) The more popular exposition of the above results is here: Unexpected Regularities in the Distribution of Prime Numbers (840 kB) Here is gzip-ed file: Download "primes.ps.gz" (260 kB) In the paper "Generalized Brun's constants" it is argued, that the sum of reciprocals of all consecutive primes separated by distance d is equal to 4c_2 d \prod_{p\mid d} {p-1\over p-2}. M.Wolf, Generalized Brun's constants (580 kB) Here is gzip-ed file: "brun_gen.ps.gz" (180 kB) In the paper "First Occurrence of a given gap between consecutive primes" the formula for the smallest prime such, that the next prime will be in the distance d is conjectured and compared with the results of the computer search: First Occurrence of a given gap between consecutive primes (200kB) Here is gzip-ed file: "firstocc.ps.gz" (68kB) On the similar subject you can read the paper by Thomas Nicely. In this paper the fractal structure on the set of prime numbers is described: Download On the Twin and Cousin Primes (0.5 MB) Here is gzip-ed file: "twins_ps.ps.gz" (110 kB) Download fig.1b (770 kB) Download fig.1c (1.3 MB) In this paper the analog of the Skewes number for twins is considered: An Analog of the Skewes Number for Twins (100 kB) Here (server in USA) you can find the paper "Jumping Champions" (at this web site in Poland) written by Andrew Odlyzko , Michael Rubinstein and me. It is about champions - the most often occuring gaps between consecutive primes. The most often occuring gaps are "primorials", i.e. products of consecutive primes. For example 6=2x3, 30=2x3x5, 210=2x3x5x7. If Dn denotes n-th champion Dn=2x3...xpn then they become most often occuring gap at N(n) which very roughly are given in the table below. Because Andrew Odlyzko has the Erdos Number 1 , hence I have the Erdos Number 2 . This paper was described by Ian Stewart in the December 2000 issue of the Scientific American on p.106. My papers are reviewed here by Matthew Watkins. I recommend his web page as a source of many very interesting articles about primes, zeta function etc. Here is a link to the weekly newspaper KURIER PLUS , where the interview with me can be found. It is in Polish and deals with chaos, determinism, Plato, nature of mathematical theorems etc and was conducted by Elzbieta Kolakowska. The pdf file of the famous paper "A Proof that Euler Missed... Apery's Proof of the Irrationality of zeta(3)" by Alfred van der Poorten.
Williams, Kenneth S.
Carleton University. Algebraic, analytic and computational number theory; binary quadratic forms and the arithmetic of fields of small degree.
Kenneth S. Williams Kenneth S. Williams williams@math.carleton.ca Professor of Mathematics Ph.D. (University of Toronto, 1965) D.Sc. (University of Birmingham, 1979) My research interests cover a broad spectrum of areas of number theory, including algebraic, analytic and computational number theory. I am particularly interested in arithmetic questions concerning binary quadratic forms as well as problems involving the arithmetic of fields of small degree. My current research involves extensions of the Chowla-Selberg formula which relates values of the Dedekind eta function. Publications Books School of Mathematics and Statistics Last Modified: Monday, February 14, 2000 9:22 PM. Suggestions and comments to: webmaster
Williams, Hugh
University of Calgary. Computational number theory, cryptography and the design and development of special-purpose hardware devices.
Hugh C Williams Hugh C. Williams iCORE Chair, Algorithmic Number Theory and Cryptography Professor, Department of Mathematics Statistics , University of Calgary Address: 360 Mathematical Science Building Department of Mathematics Statistics University of Calgary 2500 University Drive NW Calgary , Alberta, Canada T2N 1N4 Phone: (403) 220-6322 Fax: (403) 282-5150 E-Mail: williams@math.ucalgary.ca Website: http: www.math.ucalgary.ca ~williams My main research interests are in computational number theory, cryptography and the design and development of special-purpose hardware devices. My work in computational number theory extends from analyzing the complexity of number theoretical algorithms to actually implementing and testing such algorithms. I am also interested in developing parallel algorithms for solving certain number theoretic algorithms, particularly regulator and class number computation in real quadratic number fields. Research Interests: Computational number theory Cryptography Design and development of special-purpose hardware devices History of mathematics and computation Publications Biographical Information Centre for Information Security and Cryptography ( CISaC ) Photography Presentation - Sieve Pictures
Wilson, Stephen M. J.
University of Durham. Galois module structure; Knot modules; Virasoro characters and ray class groups.
Dr S M J Wilson
Wang, Tzu-Yueh Julie
Academica Sinica. Diophantine problems and Nevanlinna theory.
Tzu-Yueh Julie Wang Tzu-Yueh Julie Wang @@Julie Wang received her B. S. degree from the Department of Mathematics of National Tsing-Hua University. After her graduation, she worked in the Institute of Mathematics of Academia Sinica as reaserch assistant for two years. She studied in Purdue University in 1990. One year later, she transferred to the University of Notre Dame and received her Ph.D. in 1995. She then taught in the University of Texas at Austin as an instructor for one year. She is now an assistant research fellow in Academia Sinica. @@Her major research interest is number theory. Especially the area related to Diophantine problems and Nevanlinna theory. @@ Publications The truncated second main theorem of function fields, Journal of Number Theory, 58(1996), 137-159. An effective Roth's theorem of function fields, The Rocky Mountain Journal of Mathematics, 26(1996), 1225-1234. S-integral points of Pn-{2n+1 hyperplanes in general position} over number fields and function fields, Transactions of the American Mathematical Society, 348(8)(1996), 3379-3389. (With Jing Yu) On class number relations over function fields, Journal of Number Theory, to appear. A generalization of Picard's theorem with moving targets, Complex Variables Theory and Application, to appear. S-integral points of projective spaces omitting hyperplanes over function fields of positive characteristic, preprint. Generalized Cartan's conjecture and effective Wirsing's theorem over function fields, preprint. A note on Wronskians and ABC theorem for function fields of positive characteristic, preprint. [ Chinese | Home | Research Staff ]
Walling, Lynne
University of Colorado at Boulder. Number theory.
New Page Lynne Walling Professor Ph.D. Dartmouth, 1987 Office: Math 208 E-mail: walling@euclid.colorado.edu Mailing address: Lynne Walling Department of Mathematics University of Colorado at Boulder Campus Box 395 Boulder, CO 80309-0395 USA Phone: (303)-492-0249 Fax: (303)-492-7707 Research interests: Number theory Back to the top of the page
Washington, Lawrence C.
University of Maryland. Number theory, cyclotomic fields, elliptic curves, cryptology.
Homepage of Lawrence C. Washington Homepage of Lawrence C. Washington Lawrence C. Washington Professor University of Maryland Mathematics Department Office: 4415 Phone: 301-405-5116 To see email address, put cursor here and look at bottom ofpage Office Hours: Tuesday: 1:30-2:30 Thursday: 3-4 Some useful links: Math 340 Course Web page Cryptography R.I.T. Web page Cryptography Book - The Web page for the book Introduction to Cryptography with Coding Theory Cyclotomic Fields Book - The Web page for the book Introduction to Cyclotomic Fields Elliptic Curves Book - The Web page for the book Elliptic Curves: Number Theory and Cryptography Research interests: Number theory, cyclotomic fields, elliptic curves, cryptology My curriculum vitae Other interests: Running, playing bassoon
Ward, Thomas
University of East Anglia. Dynamical properties of commuting maps and algebraic dynamical systems, dynamical realization of integer sequences and other connections between number theory and dynamical systems.
Dr. Thomas Ward, MTH, UEA Dr. Thomas Ward School of Mathematics, University of East Anglia, Norwich, England, NR4 7TJ Tel: +44 (0) 1603 592848 Fax: +44 (0) 1603 593868 Email: T.Ward@uea.ac.uk Web page: http: www.mth.uea.ac.uk ~h720 Room: S0.24 Staff list , Maths Home Page This home page is maintained by webmaster@mth.uea.ac.uk . Generated 3 8 2005
Weissman, Martin H.
University of California, Berkeley. Galois representations.
Marty's Home Page Marty's Home Page You have reached the home page of Marty Weissman. I am an NSF postdoctoral fellow in mathematics at the University of California, Berkeley . Work address: Department of Mathematics, 970 Evans Hall, University of California, Berkeley, CA 94720. Office: 1067 Evans Hall. Phone: (510)642-2149 E-mail: marty@math.berkeley.edu Curriculum Vitae . Kayaking Pictures ! Mathematics Papers: D4 Modular Forms , to appear in the American Journal of Mathematics. This paper discusses modular forms on two groups of type D4, examples of Langlands functoriality, an octonionic Jacquet-Langlands correspondence, and a Siegel-Weil type formula. Here is a preprint , also available on the ArXiv. The Fourier-Jacobi Map and Small Representations . There are two available versions of this paper. My Ph.D. thesis , which includes an introduction motivating the theory of small representations. This was supervised by Benedict Gross and Gordan Savin. This paper has been published in the AMS Journal of Representation Theory . The published version is considerably shorted than my Ph.D. thesis, since it is single-spaced and lacks an extensive introduction. The published article also lacks a few small errors typos that exist in the thesis. Icosahedral Galois Representations and Modular Forms . This was my undergraduate senior thesis . I perform some numerical computations to provide evidence that an even two-dimensional Galois representation of icosahedral type is associated to a Maass form. This was supervised by Andrew Wiles and Peter Sarnak. Eisenstein Series over a Quadratic Imaginary Field . This exposition, my undergraduate junior paper , is based on the notes and supervision by Goro Shimura. Teaching Links: Math 115, Fall 2005 (Undergraduate Number Theory) Math 113, Spring 2005 (Undergraduate Abstract Algebra) Math 254A, Fall 2004. (Graduate Number Theory) Notes and exercises on Tate's thesis . The Bay Area Mathematics Project . Math Resources: Mathscinet reviews , The ArXiv , Garrett's notes , Number Theory Web . Math Departments: Berkeley , Harvard , Princeton , Stanford , MIT , UCSD , UCLA , Utah , Michigan . News: CNN . The Onion . Non-news: Surf Forecast . Craigslist .
Waldschmidt, Michel
Paris VI (Universit Pierre et Marie Curie). Diophantine approximation and transcendence.
Site Michel Waldschmidt - Site Hlne Waldschmidt Site Michel Waldschmidt Site en souvenir d'Hlne
Verrill, Helena A.
Louisiana State University. Arithmetic algebraic geometry. Fundamental domain drawer and Magma code.
H. A. Verrill's homepage H. A. Verrill's homepage Click here for the frame-free version of contents of this site.
van der Poorten, Alf
Macquarie University, ceNTRe for Number Theory Research. Continued fractions and effective diophantine approximation; diphantine equations. Papers and "Notes on Fermat's Last Theorem".
Alf van der Poorten Alf van der Poorten AM E-Mail: alf@math.mq.edu.au Emeritus Professor of Mathematics . Chair, Academic Senate of the University 1986-1987; 1997-2001. Head, School of Mathematics and Physics 1980-1987 and School of Mathematics, Physics, Computing, and Electronics 1991-1996. Director, ceNTRe for Number Theory Research . If you don't mind a self-indulgent boringly long description, then by all means read Alf's background . Notwithstanding that pretentious 3rd-person stuff, it's obviously autobiographical. One shouldn't have thought that anyone cares about Alf's personal interests . Alf's rarely in his new office but can readily be contacted by . If you absolutely have to fax him, send it to +61 2 9850 8114. Recent talks as pdf display files: Continued fractions and elliptic sequences Paperfolding, automata, and rational functions Clicking here may allow you to find several of Alf's papers in pdf form. Clicking here displays 1996 versions of my most important publications. Of course, you may well be looking for stuff about Alf's book Notes on Fermat's Last Theorem . Emeritus Professor Alfred J van der Poorten AM 1 Bimbil Place Killara Australia 2071 Fax: +61 2 9850 8114 Mobile: +61 4 1826 3129 Home Phone: +61 2 9416 6026 Internet: alf@math.mq.edu.au Home Page alf@math.mq.edu.au : 10 2004
van de Woestijne, Christiaan
Mathematisch Instituut, Leiden. Algorithmic theory of quadratic forms. Publications, thesis.
Christiaan van de Woestijne Christiaan van de Woestijne Nederlands English Number Theory Group Department of Mathematics Universiteit Leiden Postal address: Drs. C.E. van de Woestijne Mathematical Institute P.O. Box 9512 2300 RA Leiden The Netherlands Office: M.I. 231 Telephone: +31 - 71 - 527 7131 Fax: +31 - 71 - 527 7101 E-mail: cvdwoest@math.LeidenUniv.nl From 1 10 2005 until 31 12 2005: Research assistant at RICAM , an institute of the Austrian Academy of Sciences Altenbergerstrae 69, A-4040 Linz, Austria Telephone: +43 (0)732 2468-5248 Fax: +43 (0)732 2468-5412 See also here . Click here for my music page. Research I'm working in number theory, with special interest in (varieties over) finite fields, symbolic computation and complexity of algorithms, and combinatorics. Currently I'm about to defend my Ph.D. thesis, which is about deterministic algorithms for solving polynomial equations in many variables over finite fields. My advisor is Prof. H.W. Lenstra, Jr.. Click here for an almost final version (in PDF). An extended abstract appeared in the Proceedings of ISSAC 2005; click here for the text. Here is a recent CV . In 1997 98, I did a research project for obtaining my Master's degree in mathematics under supervision of Dr Benne de Weger and Prof. R. Tijdeman. It was a number-theoretic project about almost-powers (integral numbers of the form axk, where a is relatively small); the question was how close we can get such numbers to each other in various constellations. My thesis (in gzipped PostScipt) is available here . In a shorter version, it appeared in two parts in the 1999 volume of Acta Arithmetica (vol. 90). In 1998 99, I did the same for my Computer Science degree, supervised this time by Dr Hendrik-Jan Hoogeboom, and Dr Crit Cremers from the department of General Linguistics. This time, I was occupied with the Delilah system, developed by Cremers and Hijzelendoorn, which is a parsing system for the written Dutch language. The problem was firstly to relate the Delilah system to grammar formalisms currently studied in theoretical computer science, and secondly to estimate the time and space complexity of the parsing system. You can find my results in my thesis (also in gzipped PostScript). Talks Deterministic equation solving in finite fields, Oberwolfach workshop on Finite Fields, December 2004 ( PDF ) Go up: [ Leiden University | Faculty of Sciences ] Last modified by Christiaan van de Woestijne on November 11, 2005.
van Frankenhuysen, Machiel
Utah Valley State College. Hyperbolic spaces and the ABC conjecture.
Machiel van Frankenhuijsen -- Official Web Site Home Classes Downloads Bibliography CurriculumVitae ContactInformation Machiel van Frankenhuijsen Machiel van Frankenhuijsen is currently an Assistant Professor at Utah Valley State College . Here you will find: information about the classes I teach . downloadable stuff , such as most recent papers and some older ones that are now available in electronic form. a complete and up-to-date bibliography that points to downloadable papers. To get in touch with Machiel van Frankenhuijsen, see the " Contact " section. Copyright 2005 Machiel van Frankenhuijsen. All rights reserved.
Vallentin, Frank
Hebrew University of Jerusalem. Geometry of numbers; computational algebraic number theory.
Frank Vallentin Frank Vallentin Centrum voor Wiskunde en Informatica Kruislaan 413 P.O. Box 94079 1090 GB Amsterdam, The Netherlands Room: 138 Phone: +31-20-5924170 Mobile Phone: +31-63-8164387 Home: +31-20-4631188 E-mail: f.vallentin at cwi dot nl WWW: http: www-m10.ma.tum.de ~vallenti About me Research (Computational Geometry of Numbers) Teaching (Munich University of Technology)
Venjakob, Otmar
Universitt Heidelberg. Iwasawa theory of p-adic Lie extensions; arithmetic of elliptic curves, Selmer groups of abelian varieties, structure of profinite (or pro-p) groups. Publications.
venjakob Dr. Otmar Venjakob Universitt Heidelberg Mathematisches Institut Im Neuenheimer Feld 288 D-69120 Heidelberg Germany Telefon: +49-(0)6221-54-4975, Sekretariat: -5766, Telefax: -8312 Email: otmar@mathi.uni-heidelberg.de Research interests Bibliography Private Research interests Iwasawa theory of p-adic Lie extensions, i.e. structure theory of (modules over) completed group rings, Arithmetic of Elliptic Curves, Selmer groups of abelian varieties, Structure of profinite (or pro-p) groups, generalized free (co)products, e.g. fundamental groups of graphs of groups ... Bibliography On the structure of Selmer groups over p-adic Lie extensions (with Yoshihiro Ochi) Galois groups of real function fields in one variable with restricted ramification On the structure theory of the Iwasawa algebra of a p-adic Lie group On the Iwasawa theory of p-adic Lie extensions On the ranks of Iwasawa modules over p-adic Lie extensions A noncommutative Weierstrass preparation theorem and aplications to Iwasawa theory Completely faithful Selmer groups over Kummer extensions (with Yoshitaka Hachimori) Characteristic Elements in Noncommutative Iwasawa Theory The GL_2 main conjecture for elliptic curves without complex multiplication Private Casa Estudio (Kolumbien, Bogot, Straenkinder, ...)
Vajaitu, Marian
Romanian Academy of Sciences. Algebraic number theory, analytic number theory, class field theory and theory of algebraic functions.
CURRICULUM VITAE MARIAN VAJAITU Born: September 27, 1962, Colt, Romania. Address: Romanian Academy, P.O. Box. 1-764, R0-70700 Bucharest, Romania. Studies: I graduated from Department of Mathematics of Mathematics of the University of Bucharest in 1987. The title of Diploma Dissertation was "Riemann's zeta function and applications in Number Theory". The main lectures during this period are: two year a basic course in algebra, an year a basic course in real analysis, complex analysis (a semester), measure theory (a semester), two years a basic course in differential equations, an year of axiomatic and euclidean geometry, an year of differential geometry, an year of functional analysis, a supplementary year of algebra (number theory and groups theory), a course in Algebraic Geometry and one in Algebraic Topology. I studied some classical works in number theory, such as: - analytic number theory (from the books by Ingham, Eduards, Davenport, Titchmarsh, Halberstan, Baker, Bump). - algebraic number theory (from the books by Borevich and Shafarevich, H. Hasse and S. Lang). - valuations and the theory of algebraic functions (from the books by Schilling, Chevalley and Hasse). - class field theory (from the books by Hasse, Chevalley and Neurkirch). I participated also at the seminar of Number Theory lead by Professor N. Popescu devoted to algebraic number theory, analytic number theory, class field theory and theory of algebraic functions. Employment: 1987-1990 - Teacher at the High School at Petrosani, Romania (forced by the laws of former regime), since 1990 - Researcher at Institute of Mathematics, Bucharest, Romania. Fields of interest: Number theory with special interest in analytic number theory, algebraic numbers and functions, transcendental numbers, local class field theory, diofantine equations. Scientific activity: Working in the field of Number Theory, I obtained some results. Part of them are collected in some papers, from which I mention: A result dealing with some arithmetical conjectures: The conjecture of Graham " for every chain of integers 0 a_1 ... a_n" is solved for large numbers "n" by A. Zaharescu. Assuming the Riemann Hypothesis we proved that Graham's statement is true for any n\geq 10^70, in Journal of Number Theory, vol. 31, No. 1, january 1989. A problem of Selfridge which asks for the pairs (a, b) for which 2^a - 2^b | n^a - n^b for all n, INCREST preprint series in mathematics, No. 32 1989, by finding the 14 such pairs with a b. I have to say that we have seen that this problem was already solved by two (Chinese) mathematicians a few years ago. On the other hand in this preprint it is proved also that, more generally, under some simple assumptions, given a_1,...,a_k\in\ZZ^*, the set of (k + 1)-uples (\beta,(\alpha_1,...,\alpha_k )) such that \Sum_{i=1}^{i=k}(\aplha_i)\times(\beta)^{a_i} divides \Sum_{i=1}^{i=k}(\aplha_i)\times n^{a_i} for all n, is finite. Doctoral thesis in 1994 "Estimations of the ideal generated by the values of a polynomial over a Dedekind ring". A finiteness theorem for a class of exponential congruences (to appear in Proc. A.M.S.). The ideal generated by the values of a polynomial over a Dedekind ring, Rev. Roumaine Math. Pures Appl.,42 (1997), 155-161. An inequality involving the degree of an algebraic set, Rev. Roumaine Math. Pures Appl., 43(1998), 451-455. Uniform distributions in local fields (to appear). AWARDS: 2001 PRIZE ``GH. LAZAR'' OF THE ROMANIAN ACADEMY FOR MATHEMATICS. LIST OF PAPERS Graham's Conjecture under Riemann Hypothesis, J. Number Theory, vol.31, No.1, 1989. (With C. Cobeli and A. Zaharescu.) MR0978101 (90c:11064). Doctoral thesis, Estimations of the ideal generated by the values of a polynomial over a Dedekind ring, 1994. The ideal generated by the values of a polynomial over a Dedekind ring, Rev. Roumaine math. pures appl., 42(1997), 1--2, 155--161. MR1650032 (99m:13037). An inequality involving the degree of an algebraic set, Rev. Roumaine math. pures appl., 43(1998), 3--4, 451--455. MR1845541 (2002e:13039). A finiteness theorem for a class of exponential congruences, Proc. of the American Math. Soc., 127(1999), no.8, 2225--2232. (With A. Zaharescu.) MR1486757 (99j:11003). The sequence $n!\pmod p$, Journal of the Ramanujan Math. Soc., 15(2000), no.2, 71--90. (With C. Cobeli and A. Zaharescu.) MR1754715 (2001g:11153). Average estimates for the number of tuples of inverses $\pmod p$ in short intervals, Bull. Math. Soc. Sc. Math. Roumanie, Thome 43(91), no.2, 2000, 155--167. (With C. Cobeli and A. Zaharescu.) MR1881326 (2002k:11168). Uniform distributions in $p-$adic fields. An Erdos--T\'uran inequality, Buletin Stiintific--Univ. Pitesti, Seria Matematica si Informatica, Nr.5(2000), 1--7. (With A. Zaharescu.) The analytic continuation problem of $p-$adic $L-$functions, Math. Reports, vol.2(52), no.3(2000), 379--389. (With A. Zaharescu.) MR1889620 (2003b:11130). Exponential sums and their role in number theory (I), Rev. Roumaine 45, nr.6(2000), 1035--1049. (With A. Zaharescu.) MR1886536 (2002m:11076). An Erdos--T\'uran inequality in $p-$adic fields, Math. Reports, vol.2(52), no.2(2000), 243--252. (With A. Zaharescu.) MR1890979 (2003a:11093). Integer points unusually close to elliptic curves, Math. Portugaliae vol.58, Fasc.2(2001), 211--218. (With A. Zaharescu.) MR1836263 (2002e:11047). Equidistribution of rational functions of primes $\pmod q$, Journal of the Ramanujan Math. Soc. vol.16, no.1(2001), 63--73. (With C. Cobeli and A. Zaharescu.) MR1824884 (2002b:11102). Integer points near hyperelliptic curves, C.R.Math.Rep. Acad.Sci. Canada, vol.23(2001), 84--90. (With A. Zaharescu.) MR1852803 (2002e:11085). $L-$functions associated to Galois orbits in $\CC_p$, Math. Reports, vol.3(53), nr.1(2001), 83--89. (With A. Zaharescu.) MR1887188 (2003d:11175). Groups of isometries on ultrametric spaces, Bull. Math. Soc. Sc. Math. Roumanie, Thome 44(92), no.2(2001), 183--191. (With A. Zaharescu.) MR2015104 (2004i:20006). The change of space problem for metric locally constant functions, Buletin Stiintific-Univ. Pitesti, Seria Matematica si Informatica, Nr.7(2001), 179--183. (With A. Zaharescu.) Galois groups with metric constraints, Bull. Math. Sci. Roumaine, vol.44(92), no.3(2001), 211--219. (With A. Zaharescu.) MR2013339 (2004g:11105). Uniform distribution of polynomial sequences in $p-$adic fields, Buletin Stiintific--Univ. Pitesti, Seria Matematica si Informatica, no.7(2001). (With A. Zaharescu.) Exponential sums and their role in number theory (II), Rev. Roumaine 47(2002), 135--148.(With A. Zaharescu.) MR1978194 (2004e:11084). Integer points close to algebraic curves, Journal of the L.M.S., vol.65(2002), no.1, 10--26. (With F.P. Boca and A. Zaharescu.) MR1875132 (2003b:11067). On the set $ax+bg^x \pmod p$, Math. Portugaliae, vol.59, Fasc.2(2002), 195--204. (With C. Cobeli and A. Zaharescu.) MR1907414 (2003d:11113). Differences between powers of a primitive root, Internat. Journal Math. Sci., vol.29, no.6(2002), 325--331. (With A. Zaharescu.) MR1897859 (2003e:11002). Chains of metric invariants over $p-$adic fields, Acta Arithmetica, 103, 1(2002), 27--40. (With A. Popescu, N. Popescu and A. Zaharescu.) MR1904892 (2003g:11138). Generalization of a theorem of Steinhauss, Colloq. Math., vol.92(2002), no. 1--2, 257--266. (With C. Cobeli, G. Groza and A. Zaharescu.) MR1899442 (2003h:11082). Distribution of values of rational maps on the ${\bf F}_p-$points on an affine curve, Monatshefte fur Mathematik, 136(2002), 81--86. (With A. Zaharescu.) MR1908082 (2003f:11089). Character sums and pair correlations, Demonstratio Math., vol.35, no.2(2002), 225--232. (With A. Zaharescu.) MR1907295 (2003d:11123). A class of algebraic--exponential congruences modulo $p$, Acta Math. Univ. Comenianae, 71(2002), no.1, 113--117. (With C. Cobeli and A. Zaharescu.) MR1943018 (2003m:11208). A class of irreducible polynomials, Journal of the Ramanujan Math. Soc. vol.17(2002), no.3, 161--172. (With M. Cavachi and A. Zaharescu.) MR1925187 (2003g:12002). Polynomial--exponential equations modulo $p$, Buletin Stiintific-Univ. Pitesti, Seria Matematica si Informatica, Nr.8(2002), 183--188. (With C. Cobeli and A. Zaharescu.) Metric locally constant functions, Acta et Commentationes Universitatis Tartuensis de Mathematica, vol.6(2002), 29--36. (With A. Zaharescu.) MR1962874 (2004d:11117). Distinct gaps between fractional parts of sequences, Proc. A.M.S., vol.130, no.12(2002), 3447--3452. (With A. Zaharescu.) MR1918819 (2003d:11112). Distribution of gaps between the inverses $\pmod q$, Proc. Edinburgh Math. Soc., 46(2003), 1--19. (With C. Cobeli and A. Zaharescu.) MR1961820 (2004a:11105). Sequences of values of power series over $p-$adic fields, Revue Roumaine, 48(2003), 2, 211--216. (With A. Zaharescu.) MR1999021 (2004i:11089). Nonarchimedean valuation on $\RR$ and $\CC$, Math. Reports, 5(55), 3(2003), 267--273. (With A. Zaharescu.) On the unicity of immediate maximal extensions of valued fields, Math. Journal of Ibaraki Univ., vol.35(2003), 29--33. (With A. Zaharescu.) MR2040538. An irreducibility criterion for polynomials in several variables, Acta Math. et Informatica Univ. Ostraviensis, to appear. (With M. Cavachi and A. Zaharescu.) On the existence of trace for elements of $\CC_p$, Algebras and Representation Theory, to appear. (With N. Popescu and A. Zaharescu.) Some asymptotic formulas involving primes in arithmetic progression, Commentarii Math. Univ. St. Pauli, Japan, Vol. 53, No. 1(2004), 23--35. (With C. Cobeli, L. Panaitopol and A. Zaharescu.) Regularization on ordered sheaves, Revue Roumaine math. pures appl., {\bf 43}(2004), 3, 303--309. (With A. Zaharescu.) On Krasner analytic functions and the $p-$adic Mellin transform, Math. Journal of Ibaraki Univ. submisa. (With A. Zaharescu.) Transformation formulas for $L-$functions associated with Galois orbits in $\CC_p$, Revue Roumaine, to appear. (With A. Zaharescu.) Primitive arcs on elliptic curves, Revue Roumaine, to appear.
Voelklein, Helmut
University of Florida, Gainesville. Galois theory. Books, papers, software.
Helmut Voelklein NAME: Helmut Voelklein ADDRESS: Department of Mathematics University of Florida 436 Little Hall Gainesville, FL 32611-8105 PHONE: (352) 392-0281 ext.287 FAX: (352) 392-8357 E-MAIL: helmut@math.ufl.edu Research Area: GALOIS THEORY Galois theory and group theory originated with the breakthrough of E. Galois (1811 - 1832). He considered the ancient problem of finding a general formula for the roots of a (separable) polynomial f(x) of any degree n. In the case n=2, there is the well-known formula for a quadratic equation, with its plus-minus symmetry. For n=3 and n=4 there are similar, but much more complicated formulas. Their symmetries also get more complicated. It was Galois' idea to consider the 'group' of these symmetries as an independent object. It can be defined without actually knowing a formula, as the group of permutations of the roots that preserve all algebraic relations (in modern terminology, the group of permutations of the roots that extend to automorphisms of the field generated by the roots). As first application, Galois proved that there is actually no general formula for n at least 5. B. Riemann (1826 -1866) linked the algebraic theory of Galois with analytic topological notions of monodromy and Riemann surfaces. This is Riemann's Existence Theorem. The basic idea is to study how the roots of a polynomial behave under a continuous deformation of the coefficients. Modern developments like the classification of finite simple groups and the advent of computer algebra have given new impetus to Galois theory. One manifestation was the Constructive Galois Theory Workshop, MSRI Berkeley, Oct. 99 Publications Books Groups as Galois Groups: An Introduction Cambridge Studies in Advanced Mathematics 53, Cambridge University Press 1996. Edited Conference Proceedings Managing editor of the Proceedings of the 1996 "UF Galois Theory Week", appeared as "Aspects of Galois Theory", edts. D. Harbater, P. Mueller, J. G. Thompson, H. Voelklein, London Math. Soc. Lect. Notes 256, Cambridge University Press 1999. postscript file of introduction Proceedings of the 1993 Seattle AMS Summer Conference ``Recent Developments in the Inverse Galois Problem,''edts. S. Abhyankar, W. Feit, M. Fried, H. Voelklein, AMS Contemporary Math Series 186, 1995. Selected papers (with M. Fried), The inverse Galois problem and rational points on moduli spaces, Math. Annalen 290 (1991), 771-800 (with M. Fried), The embedding problem over a Hilbertian PAC-field, Annals of Math. 135 (1992), 469-481 PSL(2,q) and extensions of Q(x), Bulletin AMS 24 (1991), 145-153 Rigid generators of classical groups, Math. Annalen 311 (1998), 421-438 (with J. Thompson), Symplectic groups as Galois groups, J of Group Theory 1 (1998), 1-58. (with K. Strambach), On linearly rigid tuples, Crelle J. 510 (1999), 57--62 A transformation principle for covers of P^1, Crelle J. 534 (2001), 155--168 Click here for a list of all papers Software for braid orbit computation Click here to download the tar archive of program files Unpack with "tar xvf braid.tar". The files appear in a subdirectory called "braid". Open a GAP window and type Read("assemble.g"). This reads all the program files. The following paper explains how to use the package. A GAP package for braid orbit computation, and applications by K. Magaard, S. Shpectorov and H. Voelklein, to appear in Experimental Math. Calculus 2 fall 2004 syllabus Introduction to Numerical Linear Algebra (Spring 2004) Course description grading policy, office hours etc. Cryptography course spring 2003 syllabus Luminy lecture March 2004 PDF file of manuscript Former PhD students Tony Shaska, PhD March 2001 (Now assistant professor (tenure track) at the U of Idaho). Vishwa Krishnamoorthy, PhD April 2001. Conferences at the University of Florida Galois Theory Conference in honor of John Thompson's 70th birthday, November 2002 Computational Algebra Workshop, March 2003
Venkov, Boris
Laboratory of Algebra and Number Theory, Petersburg Department of Steklov Institute of Mathematics. Contact information.
Boris Venkov [Switch to Russian] Boris Venkov Laboratory of Algebra and Number Theory Petersburg Department of Steklov Institute of Mathematics 27, Fontanka, 191011, St.Petersburg, Russia Phone: +7 (812) 312-40-58 Fax: +7 (812) 310-53-77 Email: bvenkov@pdmi.ras.ru URL: Personal Page [Switch to English] - ... 191011, . ., 27 : +7 (812) 312-40-58 : +7 (812) 310-53-77 Email: bvenkov@pdmi.ras.ru URL:
Viola, Carlo
Universit di Pisa. Contact information.
Carlo Viola's Home Page Prof. Carlo Viola Address: Dipartimento di Matematica Universit di Pisa Via Buonarroti 2 56127 Pisa (Italy) Telephone: +39 050 2213217 E-mail: viola at dm.unipi.it Number Theory Group home page Department of Mathematics of the University of Pisa
Vazzana, Tony
Truman State University. Contact information and teaching schedule.
index Tony Vazzana Associate Professor of Mathematics How to contact me Email address: tvazzana@truman.edu Office: Violette Hall 2262 Office Phone Number: (660) 785-4284 Fax Number: (660) 785-4251 Postal Address: Division of Mathematics and Computer Science Truman State University Kirksville , MO 63501 Fall 2005 Schedule Monday Tuesday Wednesday Thursday Friday 8:30 Math 451 Office Math 451 Office Math 451 Hours Hours 9:30 Math 198 Math 198 Math 198 Math 198 Math 198 10:30 Office Office Math 497 Office Office Hours Hours Hours Hours 11:30 Office Office Office Hours Hours Hours 12:30 Feel free to drop by anytime, or get in touch with me if you'd like to schedule an appointment.
Vlez, William Yslas
University of Arizona. Algebraic and elementary number theory; Group theory; Field theory; Algebraic coding theory; Communication theory; Signal processing. Preprints and articles on educational issues.
W.Y. Velez's Homepage William Yslas Vlez Bill Vlez in 1965 Bill Vlez in 1995 Personal Information Curriculum Vitae Math 115a Articles Permutations of the positive integers with restrictions on the sequence of differences "University Faculty: Priming the Pump or Lying in Ambush?" "Integration of Research" "Academic Advising as an Aggressive Activity" "Some Thoughts on the Funding of Mathematics" "The Algebra Initiative Colloquium" "The Research Mathematician as Storyteller" Powerpoint Presentations James Leitzel Lecture, MathFest, August 6, 2005 Notes for Power Point James Leitzel Lecture Increasing the Number of Mathematics Majors-presentation to Engaging Young Mathematicians, Washington, DC, August 12, 2005 Notes for the Engaging Young Mathematicians workshop Patents Method and Apparatus For Suppressing Interference From Bandspread Comunication Signals, J. W. Bond, T. Schlosser, W. Y. Vlez, (1991), Patent 5, 495, 497, Patent Date: 27 Feb., 1996 Method and Apparatus For Suppressing Linear Amplitude Interference From Bandspread Communication Signals, J. W. Bond, W. Y. Vlez, Patent 5, 495, 496, Patent date: 27 Feb., 1996. Simplified Interference Suppressor, James W. Bond, Stefen Hui, W. Y. Vlez, Patent 6,072,845, Patent date: 6 June 2000. Adaptive Processor Integrator for Interference Suppression, James W. Bond, Thomas W. Schlosser, W. Y. Vlez, Patent 6,173,167, Patent date: 9 January 2001 Some Links SACNAS HOMEPAGE
Voight, John
University of California, Berkeley. Quadratic forms, perfect numbers.
John Voight John Voight Visiting Scholar Magma Research Group School of Mathematics and Statistics University of Sydney Address: Magma Group Department of Mathematics and Statistics F07 University of Sydney, NSW 2006 Australia Office: Room 631 Carslaw Building Email: jvoight@gmail.com Phone: +61 2 9351 5792 Homepage: http: magma.maths.usyd.edu.au ~voight Research Interests: Arithmetic algebraic geometry: Modular curves and moduli spaces, elliptic curves, computational and algorithmic aspects Number theory: Algebraic number theory, quaternion algebras, Arakelov theory, zeta functions of varieties over finite fields, cryptography and coding theory Publications: Quadratic forms that represent almost the same primes, math.NT 0410266 , submitted to Math. Comp. Algorithms for quaternion algebras, in preparation. Computing CM points on Shimura curves arising from compact arithmetic triangle groups, in preparation. Curves over finite fields with many points: an introduction, Computational aspects of algebraic curves , ed. Tanush Shaska, Lecture notes series on computing, vol. 13, World Scientific, Hackensack, NJ, 2005, 124-144. Quadratic forms and quaternion algebras: Algorithms and arithmetic, Ph.D. thesis, University of California, Berkeley, 2005. [ DVI ] [ PDF ] [ PS ] On the nonexistence of odd perfect numbers, MASS Selecta: Teaching and learning advanced undergraduate mathematics , Svetlana Katok, Alexei Sossinsky, and Serge Tabachnikov, eds., American Mathematical Society, Providence, RI, 2003, 293-300. Job Application: AMS Standard Cover Sheet Curriculum Vitae Summary Research Statement Publication List Teaching Statement Teaching Portfolio Teaching: Math 110: Linear Algebra (Spring 2005) Math 115: Introduction to Number Theory (Summer 2004) Math 1A: Calculus (Spring 2004) Math 250B: Multilinear Algebra (Spring 2003) Math 195: Cryptography (Spring 2002) Math 1B: Calculus (Fall 2001) Notes and Expository Articles: Perfect numbers: An elementary introduction [ DVI ] [ PDF ] [ PS ] Introduction to stacks [ DVI ] [ PDF ] [ PS ] Toric surfaces and continued fractions [ DVI ] [ PDF ] [ PS ] Oberwolfach seminar on Explicit Algebraic Number Theory [ Link to Notes ] Aspects of complex multiplication (notes from Zagier) [ DVI ] [ PDF ] [ PS ] Introduction to group schemes (notes from Schoof) [ DVI ] [ PDF ] [ PS ] Rational and integral points on higher dimensional varieties (notes from AIM) [ Link to Notes ] Algebraic geometry (notes from Hartshorne) [ DVI ] [ PDF ] [ PS ] The following counter is due to digits.com .
van der Straten, Didier
Prime number theory.
Researches in Prime Number Theory RESEARCHES IN PRIME NUMBER THEORY : Retired after 30 years with IBM, I continue working on favorite math hobby : Prime Numbers. Just tenderfoot in creating a Web page. Lost in how to program on a P.C. but following a cure. Three main claims of originality in my sofar searches. 1. Algorithmic formula for smoothened pi(x), and hence for the prime number density. Results up to 10^9, with deviations less than 800. Still many questions ! details , table example 2. Ulam's spirals study : sound explanation as to why some "parallel to diagonal" rows display rather higher prime density. ulam expl (added November 17, 2004) 3. Contribution to the study of Goldbach conjecture : a formula and a table allowing to evaluate the number of Golbach partitions vs 2n. Goldbach text , Golbach partitions count evaluation table . If interested in more, e-mail to me : vdstrat@attglobal.net. (and I will reply or produce further pages). I owe acknowledgments to many prime number theory contributors discovered thru web pages : Chris Caldwell, Marek Wolf, Matthew Watkins, Thomas Nicely... (I will update as my memory recalls me). Last update Nov 17, 2004 geovisit();
Vsemirnov, Maxim
Sidney Sussex College, Cambridge (on leave from Steklov Institute of Mathematics, St. Petersburg). Diophantine equations, Hilbert's Tenth Problem; linear groups.
Maxim Vsemirnov's homepage Maxim Vsemirnov Senior Researcher at Steklov Institute of Mathematics at St. Petersburg Associate Professor at St. Petersburg State University . a former Fellow of Sidney Sussex College , University of Cambridge . Address Laboratory of Mathematical Logic of Steklov Institute of Mathematics at St. Petersburg 27, Fontanka, St.Petersburg, 191023, Russia Phone: +7 (812) 571-43-92 FAX: +7 (812) 310-53-77 Email: vsemir at pdmi.ras.ru Keywords to areas of interest Number theory: Diophantine equations, Hilbert's Tenth Problem. Algebra: linear groups, Hurwitz groups, permutations. Combinatorics: permutations, combinatorial identities, spherical codes. Information for students (in Russian only). Other Information
Villegas, Fernando Rodriguez
University of Texas at Austin. Special values of L-series (in particular, those related to the conjectures of Birch Swinnerton-Dyer and Bloch Beilinson), the arithmetic of elliptic curves and modular forms.
Home Page of Fernando Rodriguez Villegas Fernando Rodriguez Villegas Address: Department of Mathematics, UT Austin, Austin, TX 78712 Phone: (512) 471-1137 Office: RLM 9.164 Fax: 512-471-9038 E-mail: villegas@math.utexas.edu CURRICULUM VITAE dvi, ps, pdf. RESEARCH I am interested in special values of L-series (in particular, those related to the conjectures of Birch-Swinnerton-Dyer and Bloch-Beilinson), the arithmetic of elliptic curves and modular forms. I am part of the Number Theory group here at UT Austin. You can find more details in my research page. CONFERENCES The upcoming Arizona Winter School will take place in Austin on March 13 - 17, 2004. TEACHING FALL 2000 Arithmetic of Elliptic Curves SPRING 2002 Topics in K-theory and L-functions (at Harvard) FALL 2002 Representation of groups SPRING 2003 Math, Puzzles and Computers FALL 2003 Algebra SPRING 2004 Math, Puzzles and Computers FALL 2004 Representation of finite groups SPRING 2005 Math, Puzzles and Computers FALL 2005 Experimental Number Theory OTHER Movie Night Last updated Send questions, comments to villegas@math.utexas.edu . Go to UT Math home page This page has been visited times since August 25, 1997
Vatsal, Vinayak
University of British Columbia. Arithmetic of elliptic curves, L-functions. Papers and preprints.
V. Vatsal's Homepage Vinayak Vatsal University of British Columbia Department of Mathematics Vancouver, BC V6T 1Z2 CANADA office: Room 234, Mathematics Building phone: 604-822-2237 fax: 604-822-6074 Office Hours: Wednesday 1-3. Math 313 Homepage A few links: Some of my papers and preprints The Langlands Project (edited by Bill Casselman ) The NUMDAM project Gary Gray's Macintosh TeX LaTeX page Some reasons why I like Vancouver
Vaserstein, Leonid N.
Penn State University. Classical groups over rings and algebraic K-theory; Waring's problem, Diophantine equations, cubic surfaces. Publications.
Home of L.N.Vaserstein Home Page of Leonid N. Vaserstein Professor of Mathematics Department of Mathematics Penn State University University Park PA 16802-6401 Resume Research Publications Algebra Number Theory 215 MB (814) 8630584 vstein@math.psu.edu Graduate Students Teaching Advising Pictures math links Last modified: Wednesday, 06-Jul-2005 10:44:37 EDT
Vnnen, Keijo
University of Oulu. Diophantine approximations and transcendence; error-correcting codes.
Homepage of professor Keijo Vnnen [ University of Oulu ] [ Faculty of Science ] [ Department of Mathematical Sciences ] [ Personnel ] Keijo Vnnen Professor, Head of the department Contact information E-mail address: keijo.vaananen@oulu.fi Room number: M232 Phone number: 08-553 1741 (work) 040-7300 547 (mobile phone) 08-553 1730 (fax) Research interest: Diophantine approximations and transcendence. Error-correcting codes. Publications Teaching
van Luijk, Ronald
University of California Berkeley. Algebraic geometry, algebraic number theory, arithmetic geometry and related topics. Catalogue of algebraic surfaces.
Ronald van Luijk [ Graduate Students | Mathematics | UC Berkeley | University of California ] Ronald van Luijk Office Hours: not this year Department Fax: (510) 642 8204 E-Mail: rmluijk (at) gmail (dot) com Department of Mathematics 3840 University of California Berkeley, CA 94720-3840 USA Though I have graduated from UC Berkeley, this webpage is still located there, while I am affiliated with CRM, Montreal, and MSRI, Berkeley, during the fall of 2005 and the spring of 2006 respectively. Application Material I am applying for a position starting mid 2006. My application material can be found here . Theses My graduate thesis (2005) is titled Rational points on K3 surfaces . My undergraduate thesis (2000) is titled On perfect cuboids (zipped). Papers and Presentations Papers and slides from presentations can be found here . Catalogue of Surfaces I intend to start a catalogue of algebraic surfaces , that are of interest to number theorists because of their rational points. The catalogue will include references, so that if "new" surfaces pop up, they can be compared with other surfaces, that have already been analysed. As for now, the catalogue doesn't contain many surfaces yet. Please e-mail me about any surfaces you've encountered and or worked on, that might be of interest. Teaching Math 1B (Calculus), spring 2001 Math 1A (Calculus), fall 2001 Math 110 (Linear Algebra), spring 2002 Math 55 (Discrete Mathematics), summer 2002 Math 1B (Calculus), spring 2003 Math 1B (Calculus), spring 2005 Links People Frits Beukers James Milne Bjorn Poonen Bart de Smit Peter Stevenhagen Bernd Sturmfels Arthur Baragar Mathematical Papers and Tables AMS MathSciNet Search Encyclopedia of Integer Sequences Encyclopedia of Real Numbers JStor Algebraic Number Theory Archives The Mathematical Atlas Number Theory 11D: Diophantine equations Algebraic Geometry 14J: Surfaces and higher dim's Online Manuals LaTeX GAP4 GP Pari MAGMA Maculay2 HTML MetaPost Manual MetaPost Examples More MetaPost Examples Maps Map Quest PCL Online Map Collection CIA World Factbook 2000 The Weather Channel Dictionaries OneLook Dictionary Merriam-Webster Dictionary Roget's Thesaurus Encyclopedia Britannica Geographic Names Dutch-English-Dutch A Web of Dictionaries travlang's Translating Dictionaries Van Dale More Information The weather anywhere Reisplanner NS (Dutch) Telefoongids (Dutch) Postcodeboek (Dutch) More Mathematics Number Theory Web (American Site) Pythagoras (Dutch) International Mathematical Olympiad . Currencies Pacific, graphs Financial Times, Euro Currency Converter(tm) Miscellanea PriceSCAN Jennifer's Page of Links: Language Resources Air Query This page was stolen from Alex Barnard (thanks!) and last modified at October 27, 2005.
Voloch, Felipe
University of Texas. Number theory and algebraic geometry: applications to coding theory and cryptography.
Felipe Voloch Felipe Voloch Contact Information Dept. of Mathematics University of Texas Austin TX 78712 USA e-mail: phone:(512) 471-2674 fax:(512) 471-9038 Research My research is in Number Theory and Algebraic Geometry and applications to Coding Theory and Cryptography. See my preprints or my cv . I am part of the Number Theory group here at UT. There is also a lot of information on Number Theory at the Number Theory Web . I am also a member of the Southwestern Center for Arithmetical Algebraic Geometry . I am an editor of "Ensaios Matematicos", a journal published by the Brazilian Mathematical Society . The journal aims to publish reviews and surveys of high level. Here is the call for papers . Teaching I am teaching 380C Graduate Algebra in the Fall of 2005. I am giving a lecture in the Saturday Morning Math Group on Dec. 3rd about Google . For the web pages of courses I taught in the past and other teaching information go to my course gallery .
Veys, Wim
University of Leuven. Algebraic geometry, singularity theory, applications in number theory. Papers and preprints.
veys Home Page of Wim Veys Contents Work Information Contact Information Publications with available DVI- and PS-file Previous publications Work Information Professor at the University of Leuven (K.U.Leuven), Department of Mathematics, Section of Algebra Fields of Research Algebraic Geometry, Singularity Theory, applications in Number Theory Specific Research Topics Exceptional divisor of an embedded resolution, Zeta Functions (Igusa, topological, motivic), Monodromy, configurations of curves on surfaces, Stringy invariants, Principal value integrals Ph.D.Students Dr. Bart Rodrigues : Geometric determination of the poles of motivic and topological zeta functions , may 2002 Dr. Dirk Segers : Smallest poles of zeta functions and solutions of polynomial congruences, april 2004 Jan Schepers : On stringy invariants Ann Lemahieu : On possible poles of zeta functions Filip Cools (other adviser : Marc Coppens) : On defectivity of projective varieties Lise Van Proeyen : On motivic and topological zeta functions Back to top Contact Information Address : University of Leuven, Department of Mathematics, Celestijnenlaan 200 B, B-3001 Leuven (Heverlee), Belgium. Electronic mail address : wim.veys@wis.kuleuven.be Web address : http: www.wis.kuleuven.be algebra veys.htm Office phone : (+32)16-327092 Office fax : (+32)16-327998 Back to top Publications with available DVI- and PS-file (starting from 1992) W.Veys, Reduction modulo p^n of p-adic subanalytic sets, Math. Proc. Cambridge Philos. Soc. 112 (1992), 483--486. dvi , ps W.Veys, Holomorphy of local zeta functions for curves, Math. Annalen 295 (1993), 635-641. dvi , ps W.Veys, Poles of Igusa's local zeta function and monodromy, Bull. Soc. Math. France 121 (1993), 545-598. ps W.Veys, On Euler characteristics associated to exceptional divisors, Trans. Amer. Math. Soc. 347 (1995), 3287-3300. dvi , ps J. Denef and W. Veys, On the holomorphy conjecture for Igusa's local zeta function, Proc. Amer. Math. Soc., 123 (1995), 2981-2988. dvi , ps W.Veys, Determination of the poles of the topological zeta function for curves, Manuscripta Math. 87 (1995), 435-448. dvi , ps W. Veys, Zeta functions for curves and log canonical models, Proc. London Math. Soc. 74 (1997), 360-378. dvi , ps W. Veys, More congruences for numerical data of an embedded resolution, Compositio Math. 112 (1998), 313-331. dvi , ps W. Veys, Structure of rational open surfaces with non-positive Euler characteristic, Math. Annalen 312 (1998), 527-548. dvi , ps W. Veys, The topological zeta function associated to a function on a normal surface germ, Topology 38 (1999), 439-456. dvi , ps A.Laeremans and W. Veys, On the poles of maximal order of the topological zeta function, Bull. London Math. Soc. 31 (1999), 441-449. dvi , ps W. Veys, Embedded resolution of singularities and Igusa's local zeta function, Academiae Analecta, 2001 (survey paper, 56p). dvi W. Veys, Zeta functions and 'Kontsevich invariants' on singular varieties, Canad.J.Math. 53 (2001), 834-865. dvi , ps B.Rodrigues and W. Veys, Holomorphy of Igusa's and topological zeta functions for homogeneous polynomials, Pacific J. Math. 201 (2001), 429-441. dvi , ps W. Veys, Stringy invariants of normal surfaces, J.Alg.Geom. 13 (2004), 115-141. dvi , ps B.Rodrigues and W. Veys, Poles of zeta functions on normal surfaces, Proc.London Math.Soc. 87 (2003), 164-196. dvi , .ps D.Segers and W. Veys, On the smallest poles of topological zeta functions, Compositio Math. 140 (2004), 130-144. dvi , ps W. Veys, Stringy zeta functions for Q-Gorenstein varieties, Duke Math.J. 120 (2003), 469-514. dvi , ps W. Veys, Arc spaces, motivic integration and stringy invariants, Advanced Studies in Pure Mathematics , Proceedings of "Singularity Theory and its applications, Sapporo (Japan), 16-25 september 2003" (to appear), 43p. dvi , ps , pdf W. Veys, On motivic principal value integrals, preprint (2004), 14p. dvi , ps , pdf A. Lemahieu, D. Segers and W. Veys, On the poles of topological zeta functions, Proc. Amer. Math. Soc. (to appear), 11p. dvi , ps , pdf W. Veys, Vanishing of principal value integrals on surfaces, J. Reine Angew. Math. (to appear), 19p. dvi , ps , pdf Previous Publications W. Veys, On the poles of local zeta functions for curves, Proc. first Belgian-Spanish week on Algebra and Geometry, Antwerpen 1988, 173-181. W. Veys, On the poles of Igusa's local zeta function for curves, J. London Math.Soc. 41 (1990), 27-32. W. Veys, Relations between numerical data of an embedded resolution, Amer. J.Math. 113 (1991), 573-592. W. Veys, Congruences for numerical data of an embedded resolution, Compositio Math. 80 (1991), 151-169. W. Veys, Relations between numerical data of an embedded resolution, Astrisque 198 200 (1991), 397-403. Back to top Other homepages of our research group : Jan Denef Raf Cluckers Dirk Segers previous members : Philippe Jacobs , Kathleen Hoornaert Last Revised: november 2005
Velani, Sanju
University of York. Number theory, ergodic theory and dynamical systems. Papers and preprints.
sanju Dr Sanju L Velani Address: Department of Mathematics University of York Heslington York YO10 5DD Room: G 011 (Goodrick College) Telephone: +44 (0)1904 434599(direct) E-Mail: slv3@york.ac.uk FAX: +44 (0)1904 433071 Royal Society `University' Research Fellow and Reader at the Department of Mathematics , University of York Research | Teaching | Research : My main research interests are number theory, ergodic theory and dynamical sysytems. Publications. Research Preprints Teaching : Currently I am not giving any courses. This page is maintained by S Velani . Last updated October 2003
Viada-Aehle, Evelina
ETH Zrich. Arithmetic of abelian varieties.
Evelina Viada's home page Evelina Viada Departement Mathematik ETH Zentrum Rmistrasse 101 CH-8092 Zrich Switzerland ++41-1-632-3662 (office phone) e-mail: viada@math.ethz.ch Preprints Slopes and Abelian Subavieties. Minimal Elliptic Isogenies. Intersecting a Curve and Algebraic Subgroups in a Product of Elliptic Curves.
Vaughan, Robert
Penn State University. Waring's problem, the Goldbach problem, the Hardy-Littlewood method, the use of "smooth" numbers, the distribution of primes, exponential sums over integer sequences, properties of the Riemann zeta-function and Dirichlet L-functions.
Bob Vaughan's Home Page Prof. R. C. Vaughan FRS Room No : 211 McAllister Telephone No. : +1 814 865-3583 E-Mail Address : rvaughan@math.psu.edu Research Interests : My main research is in number theory, that is, the study of the properties of the whole numbers, especially by the use of analytic techniques. Particular subjects of interest are Waring's problem, the Goldbach problem, the Hardy-Littlewood method, the use of "smooth numbers", i.e. numbers without large prime factors, the distribution of prime numbers, exponential sums over integer sequences such as the sequence of primes, properties of the Riemann zeta-function and Dirichlet L-functions. Curriculum Vitae Publications Some Photographs Number Theory Seminar Math 421 Fall 2004 Math 567 Fall 2003 Math 571 Fall 2004
Valle, Brigitte
Universit de Caen. Works focused on analysis of algorithms. Includes research papers, preprints, and related links.
Brigitte Valle Brigitte Valle Directrice de Recherche Research Director Brigitte.Vallee@info.unicaen.fr Bureau Office: S3, 381 Btiment Building: Sciences 3 Informatique, Universit de Caen Bd Marchal Juin F-14032 Caen Cedex (France) Tel: +33 (0)2 31 56 74 81 Fax: +33 (0)2 31 56 73 30 Activits Activities Recherche. Ma recherche est dcrite ici . Elle se situe en analyse d'algorithmes --en arithmtique et en thorie de l'information notamment-- avec une composante forte lie aux systemes dynamiques Voir ici la page de l'quipe Algorithmique Caen, du Groupe Analyse Dynamique d'Algorithmes , et celle de l'Action spcifique Systmes dynamiques et modlisation en algorithmique (que j'ai coordonne avec Christiane Frougny et Jean Mairesse). Je suis galement associe au Projet Algorithmes de l'INRIA et au groupe de travail ALEA du G.D.R. ALP. Je suis membre du comit de pilotage de la srie des ateliers internationaux Analysis of Algorithms. (Nous avons organis la runion de Tatihou en 2001.) Research. My own research is described here . The main theme is analysis of algorithms , most notably in the areas of computational number theory and information theory, this with a strong component related to dynamical systems. See the pages of the Reseach Team Algorithmics at Caen, of the Dynamic Analysis of Algorithms Group , and the page of a nationwide special interest group on Dynamical Systems and Modelling in Algorithmics (which I have been coordinating together with Christiane Frougny and Jean Mairesse). I am also an associate member of the Algorithms Project at INRIA and an active member of the French ALEA working group. I have been a member of the Programme Committees of the international workshops Analysis of Algorithms. (we have organized the Tatihou meeting in 2001.) Enseignement. Je suis directrice de recherche au CNRS et enseigne uniquement en Mastre 2eme anne Caen et au Master Parisien de Recherche en Informatique, 2eme anne (Algorithmique). (Voir l'enseignement Caen ) Teaching. Being Research Director at the French CNRS, I enjoy a full-time research position and only teach fifth-year courses in Caen and Paris. Administration. J'ai t pour la priode 2000-2003 directrice du laboratoire GREYC . Je suis depuis 2002 charge de mission au CNRS (Dpartement STIC ). Administration. For the period 2000-2003, I have been director of the Research Laboratory GREYC . I currently serve as advisor for the "STIC" department at CNRS, being more specifically in charge of theoretical computer science and relations between CS and Maths. Liens. Les tudiants ou anciens tudiants de thse: Jrmie Bourdon , Benoit Daireaux , Julien Fayolle , Loick Lhote , Ali Akhavi , et Julien Clment (Herv Daud et Eda Cesaratto n'ont pas encore de page web); les pages de Philippe Flajolet . Links. My former and current Ph.D. students, Jrmie Bourdon , Benoit Daireaux , Julien Fayolle , Loick Lhote , Ali Akhavi , and Julien Clment (Herve'Daud and Eda Cesaratto do not seem to have a web page); the pages of Philippe Flajolet .
Vojta, Paul
University of California, Berkeley. Diophantine approximation; Nevanlinna theory, especially as related to diophantine approximation; Arakelov theory. Papers and software.
Paul Vojta Paul Vojta Office Phone (510) 642-3457 Phone messages (510) 642-6526 Fax (510) 642-8204 Email vojta@math.berkeley.edu Mail University of California, Berkeley Department of Mathematics 970 Evans Hall 3840 Berkeley, CA 94720-3840 USA Prof. Vojta's personal interests are chronicled elsewhere. Mathematical Activities Paul Vojta is a professor in the Department of Mathematics at the University of California, Berkeley . His mathematical areas of interest include: Diophantine approximation Nevanlinna theory, especially as related to diophantine approximation Arakelov theory His curriculum vitae and bibliography are available on-line. The latter contains links to TeX or PostScript copies of some of his papers. Teaching This semester (Spring 2005), Prof. Vojta is teaching: Math 256B Algebraic geometry Next semester, he will teach: Math 250A Groups, Rings, and Fields Journal Editor Prof. Vojta is an editor of Journal fr die reine und angewandte Mathematik (``Crelle's journal''). Information on submitting a manuscript is available. Programming Activities Prof. Vojta has written the following programs: For TeX: xdvi -- a previewer for .dvi files under the X Window System gsftopk -- a utility for converting PostScript fonts into .pk format For linux: qconfig -- a configuration program for the kernel. hpvptyd -- a daemon for driving ethernet printers using software for serial printers. For DOS: calvin -- a small, partial clone of the Unix vi command, available with source code in C and assembler code . There is also a calvin home page . comp -- a clone of the DOS command of the same name, written for the FreeDOS project debug -- a clone of the DOS command of the same name, written for the FreeDOS project Miscellaneous links Information on the placement exam for Math 1A is available. This may be out of date. Last updated 15 April 2005 Established April 1995
Umegaki, Atsuki
Sophia University. Arithmetic of elliptic curves. Papers, CV.
UMEGAKI, Atsuki (English) Welcome to my Home Page!!! UMEGAKI, Atsuki Research Associate, Department of Mathematics , SOPHIA University e-mail: umegaki@mm.sophia.ac.jp Last updated : March 5, 2005. to JAPANESE page Publication List Curriculum Vitae Mathematical Links Reproduction and quotation are permitted only in the case of the personal use. You may introduce URL to the public freely.
Ueda, Masaru N.
Nara Women's University. Modular forms. Papers, preprints.
Homepage of Masaru N.Ueda [For a Japanese version, please click here ] Welcome to the Homepage of M.N.Ueda This page is a link-free page. @ (Last modification:2004 10 04) Masaru N. Ueda Department of Mathematics Nara Women's University Nara, 630-8506 Japan TEL :+81-(0)742-20-3358 FAX :+81-(0)742-20-3367 E-mail: m-ueda@cc.nara-wu.ac.jp List of Publication (Oct. 04 2004 update) Preprints (May. 25 2004 update!) [ responsible ]
Urban, Eric
University of California Los Angeles. Automorphic forms and number theory.
Faculty: Eric Urban UCLA Department of Mathematics Eric Urban Hedrick Assistant Professor Education Ph.D., ENS, 1994 Research Interest Automorphic Forms, Number Theory UCLA Department of Mathematics 6363 Math Sciences, Los Angeles, CA 90095-1555 Tel: (310) 825-4701 Fax: (310) 206-6673
Ulmer, Douglas
University of Arizona. Director of the Southwestern Center for Arithmetical Algebraic Geometry.
Douglas Ulmer's Home Page Douglas Ulmer Professor of Mathematics Associate Head for the Graduate Program How to contact me: In person: Math 204 By phone: (520) 621-6861 (office) (520) 621-2068 (grad secretary) (520) 621-8322 (fax) By e-mail: ulmer@math.arizona.edu By mail: Department of Mathematics University of Arizona Tucson, AZ 85721 Current Office Hours: My office hours are Mondays and Wednesdays 3-4 in Math 204 and Fridays 1-2 in Math East 145. My calendar is online. Check for a free time and make an appointment with me or Sandy Sutton (sutton@math.arizona.edu, 621-2068), the graduate coordinator. Course pages: Course information for Complex Analysis , (Math 520A), Fall 2005 Some documents from the most recent graduate Integration Workshop My course archive . Research pages: Recent papers: Two papers showing that large ranks are ubiquitous over function fields and that small ranks in towers of function fields also occur. Geometric non-vanishing in pdf . (Published in Inventiones Mathematicae , volume 159.) Elliptic curves and analogies between number fields and function fields in pdf . (Published in MSRI Publications 49 .) Elliptic curves with large rank over function fields in various formats at ArXiv . (Published in the Annals of Mathematics , volume 155.) Slides from a talk about the second half of the analogies paper (on problems regarding the ranks of elliptic curves over number fields, cyclotomic fields, and function fields over number fields) in pdf Reviews of my articles. I'm the director of the Southwestern Center for Arithmetical Algebraic Geometry Etc.: Slides from a lecture at Dialog 04 about the Southwestern Center as an example of a large, multi-institutional project that uses NSF funding in innovative and efficient ways. Slides from a lecture at the October, 2004 meeting of the AMS Committee on Education about Long-term efforts toward VIGRE goals at the University of Arizona. The main thing I did on my 1997-98 sabbatical. Subsequent developments in that direction.
Ullom, Stephen V.
University of Illinois at Urbana-Champaign. Algebraic Number Theory, Galois Module Structure.
Stephen V. Ullom Stephen V. Ullom Professor, Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana, Illinois 61801-2975 Office: 337 Illini Hall ; (217) 333-6207; FAX: (217) 333-9576 e-mail: ullom@math.uiuc.edu General Information Ph.D. Univ. of Maryland, 1968. Areas of Specialization and Research Interests Algebraic Number Theory, Galois Module Structure of Algebraic Integers and Unit Groups, Galois Groups of Maximal Class Two Extensions with Restricted Ramification, Projective Class Groups of Integral Group Ring of a Finite Group. Selected Publications Representations related to CM elliptic curves. Math. Proc. Cambridge Philos. Soc. 113 (1993), no. 1, 71--85. (with Nigel Boston) Generators and relations for certain class two Galois groups. J. London Math. Soc. (2) 34 (1986), no. 2, 235--244. (with Stephen B. Watt) Class groups of cyclotomic fields and group rings. J. London Math. Soc. (2) 17 (1978), no. 2, 231--239. Nontrivial lower bounds for class groups of integral group rings. Illinois J. Math. 20 (1976), no. 2, 361--371. A Mayer-Vietoris sequence for class groups. J. Algebra 31 (1974), 305--342. (with Irving Reiner) PhD Students Andrew Matchett Stephen B. Watt Anupam Srivastav
Tengely, Szabolcs
University of Debrecen. Effective methods for Diophantine equations. Publications, thesis, software.
Szabi's Number Theory and Linux Distribution site Home Research Lectures Education Linux and TeX Links Photos Free counter Edit Source Contents Login Szabolcs Tengely University of Debrecen Mathematical Institute Room: M218 Phone: +36-52-512900 22800 e-mail: tengely at math dot klte dot hu "If we knew what it was we were doing, it would not be called research, would it?" - Albert Einstein Last updated at 2005-10-17 12:18 by Szabi.
Thangadurai, Ravindranathan
Indian Statistical Institute, Kolkata. Additive functions, combinatorial number theory.
Ravindranathan Thangadurai Ravindranathan Thangadurai Hi, Welcome to my personal home page. I am doing research in Number Theory which is a branch of Mathematics. I am currently attached with Stat-Math Division, Indian Statistical Institute, Kolkata. More to know about my academic interest, please follow this link My Academic Page More to know about me personally, you can click the following link. My Personal Page Everyone must have heared about the Indian genius ``Srinivasa Ramanujan'' for his works in Number Theory. If you want to know more about him click the following link. Ramanujan's Page But, even many indians may not be knowing his contemperory and very good Indian Number Theorist, namely, S. S. Pillai. The main purpose of making my home page is to create a homepage for S. S. Pillai. To learn about him and his mathematical achievements, click the following page. S. S. Pillai's Page My postal address is the following: Dr. R. Thangadurai, Stat-Math Division, Indian Statistical Institute, 203, B. T. Road Kolkata - 700108, INDIA R. Thangadurai geovisit();
Tsangaris, Panayiotis
University of Athens Panepistimioupolis. Diophantine equations.
Tsangaris, Panayiotis Panayiotis P. Tsangaris Position: Assistant Professor Research Interests: Number Theory e-mail: ptsagari@atlas.uoa.gr Phone: (+30-1-7284694) Fax: (+ 30-1-7215258) Room: E18 Postal Address: Department of Mathematics University of Athens Panepistimioupolis GR-157 84, Athens GREECE List of Selected Publications-Reviews
Towse, Christopher
Scripps College, Claremont. Arithmetic geometry and Riemann surfaces (Weierstrass points), algebraic number theory (generalized continued fractions), combinatorics (chain partitions).
Home Page of Chris Towse Christopher Towse Office: Balch 204 Phone: (909) 607-3540 E-mail: christopher.towse@scrippscollege.edu Mailing Address: Department of Mathematics 1030 Columbia Ave. Scripps College Claremont, CA 91711 USA Click here for the Scripps Math Department website. Click here for a schedule of the Claremont Colleges Mathematics Colloquium. Teaching Schedule: Fall 2005 Math 32, Calculus III. MWF, 10:00-10:50, Hum 119. Math 175, Number Theory. TTh, 2:45-4:00, Balch 220. Office Hours: Monday 11-12, Tuesday 4-5, Friday 11-12. Or by appointment. For more about the professional me , click here . Just a few Math Links Interested in the Putnam Competition? Here is the official site at Santa Clara University . Many colleges and universities put up sites each year, but they seem to change and disappear regularly. Try searching on Google to find the latest sites. Each Fall semester: If you're a Scripps student interested in the Putnam, we'll having practice sessions throughout the semester. Feel free to give me a call or email for more information. Also, Harvey Mudd has practice sessions (which you can take as a half-credit course) each fall. The Number Theory Web lists many resources. Also, Joe Silverman has a good list of math sites which are close to my own research interests. (He was my Ph.D. advisor, after all.) Everyone should be able to link to the American Mathematical Society , the Mathematical Association of America and the Association for Women in Mathematics . Did you know that Chris and Renee got married? Well, we did! Here is the page of wedding information. For some travel photos I've taken, click here . Go to the Scripps College home page. Send questions and comments to: christopher.towse@scrippscollege.edu This page was last edited on August 20, 2004. I'm working on the links!
Topuzoglu, Alev
Sabanci University. Uniformly distributed sequences; finite fields and applications; pseudo random numbers. CV.
SU Rehber Uygulamas SU Directory Application Alev Sdka Topuzolu Education: B.Sc. in Mathematics, Middle East Technical University (METU), Ph.D. in Mathematics, University of London (England), 1982. Work Experience: METU, 1980-1998; Scientific and Technical Research Council of Turkey (TBTAK), 1992-1998; Researcher: Darmstadt Technical University (Germany), during summer months, 1986-1996. Areas of Interest: Uniformly distributed sequences; finite fields and applications; pseudo random numbers. Awards: Mustafa Parlar Foundation Research and Encouragement Award, 1991. Personal Web Site
Tate, John
University of Texas. Algebraic Number Theory (local and global fields); Class Field Theory, Galois cohomology, Galois representations; L-functions and their special values; modular forms, elliptic curves and abelian varieties. Contact information.
UT - Department of Mathematics - faculty members Tate, John, Ph.D., Princeton, 1950 Sid W. Richardson Foundation Regents Chair (No. 4). Mathematics: Algebraic Number Theory. Professor. Phone: 471-7127 Office: RLM 9.134 Office hours: TBA tate@math.utexas.edu
Tubbs, Robert
University of Colorado at Boulder. Number theory. Contact information.
New Page Robert Tubbs Associate Professor Ph.D. Penn State, 1981 Office: Math 251 E-mail: tubbs@euclid.colorado.edu Mailing address: Robert Tubbs Department of Mathematics University of Colorado at Boulder Campus Box 395 Boulder, CO 80309-0395 USA Phone: (303)-492-8389 Fax: (303)-492-7707 Research interests: Number theory. Back to the top of the page
Thuswaldner, Jrg
Montanuniversitt Leoben. Analytic number theory. Papers, preprints.
Mathematik Statistik Personal ao.Univ.Prof.Dipl.-Ing.Dr.techn . Jrg M. Thuswaldner Sprechstunden: Di, Mi 10-11 email: Joerg.Thuswaldner@unileoben.ac.at Tel.: ++43 +3842 - 402 - 3805 Publications (Copyright of all papers either by the author or by the publisher) 1.) Analytic continuation of a class of Dirichlet series Abh . Math. Semin . Univ. Hamburg , 66 (1996), 281 - 287, with P. J. Grabner . 2.) q-difference equations and their applications to combinatorial problems Grazer Math. Ber ., 328 (1996), 103 - 112. 3.) The sum of digits function in number fields Bull. London Math. Soc., 30 (1998), 37 - 45. 4.) Asymptotic analysis of a class of functional equations Aequationes Math., 55 (1998), 91 - 105, with G. Derfel , R. F. Tichy and F. Vogl . 5.) Elementary properties of canonical number systems in quadratic fields in: Applications of Fibonacci Numbers, Volume 7, G. E. Bergum et al. (eds.), Kluwer Academic Publishers, (1998), 405 - 414. 6.) The fundamental Lemma of Kubilius and the Model of Kubilius in number fields in: Number Theory, K. Gyry et al. (eds.), W. de Gruyter Verlag , (1998), 489 - 499. 7.) Fractal dimension of sets induced by bases of imaginary quadratic fields Math. Slovaca , 48 (1998), 365 - 371. 8.) The sum of digits function in number fields: Distribution in residue classes J. Number Theory, 74 (1999), 111 - 125. 9.) The moments of the sum of digits function in number fields Can. Math. Bull., 42 (1999), 68 - 77, with B. Gittenberger . 10.) Summatory functions of digital sums occurring in cryptography Period. Math. Hungar ., 38 (1999), 111 - 130. 11.) An Erds-Kac Theorem for Systems of q-Additive Functions Indag . Math. (N. S.), 11 (2000) 283 - 291, with R. F. Tichy . 12.) Topological properties of two-dimensional number systems J. Thor . Nombres Bordeaux, 12 (2000) 69 - 79, with S. Akiyama. 13.) The complex sum of digits function and primes J. Thor . Nombres Bordeaux, 12 (2000) 133 - 146. 14.) On the Sum of Digits Function for Number Systems With Negative Bases Ramanujan J., 4 (2000) 201 - 220, with P. J. Grabner . 15.) Asymptotic Normality of b-Additive Functions on Polynomial Sequences in the Gaussian Number Field J. Number Theory, 84 (2000) 317 - 341, with B. Gittenberger . 16.) Fractals and Number Systems in Real Quadratic Fields Acta Math. Hungar ., 90 (2001) 253 - 269. 17.) Fractal Properties of Number Systems Period. Math. Hungar ., 42 (2001) 51 - 68, with W. Mller and R. F. Tichy . 18.) Attractors for Invertible Expanding Linear Operators and Number Systems in Z Publ . Math. Debrecen , 58 (2001) 423 - 440. 19.) Canonical number systems, counting automata and fractals Math. Proc. Cambridge Philos . Soc., 133 (2002) 163 - 182, with K. Scheicher . 20.) Neighbours of self-affine tiles in lattice tilings in: Trends in Mathematics: Fractals in Graz 2001, P. Grabner and W. Woess (eds.), Birkhuser Verlag (2002) 241 - 262, with K. Scheicher . 21.) Distribution properties of digital expansions arising from linear recurrences Math. Slovaca , 53 (2003) 1--20, with M. Lamberger . 22.) Digit systems in polynomial rings over finite fields Finite Fields Appl ., 9 (2003), 322 - 333, with K. Scheicher . 23.) On the characterization of canonical number systems Osaka J. Math., 41 (2004), 327 - 351, with K. Scheicher . 24.) On a generalization of the radix representation - a survey in: High Primes and Misdemeanours: lectures in honour of the 60th birthday of Hugh Cowie Williams, Fields Inst. Commun ., 41 (2004), 19 - 27, with S. Akiyama, T. Borbly , H. Brunotte and A. Peth . 25.) On the boundary connectedness of connected tiles Math. Proc. Cambridge Philos . Soc., 137 (2004), 397 - 410, with J. Luo and S. Akiyama. 26.) Elements of small norm in Shanks' cubic extensions of imaginary quadratic fields J. Symbolic Comput ., 38 (2004), 1471 - 1486, with P. Kirschenhofer . 27.) On the asymptotic behavior of the Laurent coefficients of a class of Dirichlet series Abh . Math. Sem . Univ. Hamburg, 74 (2004), 11 - 32, with H. Ishikawa. 28.) A survey on topological properties of tiles related to number systems Geom. Dedicata , 109 (2004), 89 - 105, with S. Akiyama. 29.) On the topological structure of fractal tilings generated by quadratic number systems Comput . Math. Appl ., 49 (2005) 1439 - 1485, with S. Akiyama. 30.) Generalized radix representations and dynamical systems I Acta Math. Hungar ., 108 (2005) 207 - 238, with S. Akiyama, T. Borbly , H. Brunotte and A. Peth . 31.) Analysis of linear combination algorithms in cryptography ACM Trans. Algorithms 1 (2005) 123--142, with P. Grabner , C. Heuberger and H. Prodinger . 32.) Waring's problem with digital restrictions Israel J. Math., to appear, with R. F. Tichy . 33.) Unimodular Pisot substitutions and their associated tiles J. Thor . Nombres Bordeaux, to appear. 34.) Waring's Problem restricted by a system of sum of digits congruences Funct . Approx. Comment. Math., to appear, with O. Pfeiffer. 35.) On Waring's and Tarry's problem with digital restrictions Proceedings of the ELAZ Conference in Mainz ( Germany , 2004), to appear, with P. Kirschenhofer und O. Pfeiffer. 36.) Generalized radix representations and dynamical systems II Acta Arith ., to appear, with S. Akiyama , H. Brunotte and A. Peth . 37.) Basic properties of shift radix systems Acta Math. Acad. Paedagog . Nyhzi . (N.S.), to appear, with S. Akiyama, T. Borbly , H. Brunotte and A. Peth . 40.) On a parameterized family of relative Thue equations submitted, together with C. Lampl and P. Kirschenhofer . (A list of integers of small norm in simplest cubic fields over $ Q( \ sqrt {-D})$ is available here ) If you are interested in one of the papers which are not downloadable, please don't hesitate to contact me via e-mail. page last modified: 12.09.2005 Jrg Thuswaldner
Tangedal, Brett
College of Charleston. Contact information.
Brett Tangedal, College of Charleston Brett Tangedal Assistant Professor Department of Mathematics College of Charleston Charleston , SC 29424 Phone: Office 803-953-5875, messages -5730, FAX -1410 Email: tangedal@math.cofc.edu Other Links The Math Department Page The Department's Faculty List The College's Faculty Home Page List
Tunnell, Jerrold
Rutgers University. Teaching information.
J.B. Tunnell's Home Page J.B. Tunnell's Home Page Mathematics 574 Information-Fall 2004 Mathematics 574 Information-Spring 2005
Teterin, Yuri
Steklov Institute of Mathematics at St. Petersburg. Contact information.
Yury Teterin [Switch to Russian] Yury Teterin Steklov Institute of Mathematics at St.Petersburg 27, Fontanka, 191011, St.Petersburg, Russia Phone: +7 (812) 312-40-58 Fax: +7 (812) 310-53-77 Email: teterin@pdmi.ras.ru URL: Personal Page [Switch to English] - ... 191011, . ., 27 : +7 (812) 312-40-58 : +7 (812) 310-53-77 Email: teterin@pdmi.ras.ru URL:
Taguchi, Yuichiro
Kyusuhu University. Drinfeld modules, Galois representations. Papers and preprints.
TAGUCHI, Yuichiro
Takloo-Bighash, Ramin
Princeton University. Distribution of rational points; Automorphic forms and representation theory. Preprints and lecture notes.
Ramin Takloo-Bighash Ramin Takloo-Bighash Assistant Professor Department of Mathematics Princeton University Princeton, NJ 08544 Phone: (609) 258-6457 Email: rtakloo@math.princeton.edu Office: 608 Fine Hall CV: dvi and pdf Research Teaching Picture was taken outside Bedford, VA (March 30, 2001) Notes from my course on Automorphic L-functions: Steven J. Miller's notes Florin Spinu's notes Please note that these notes are not complete; they have not been revised; and are heavily based on a course given by Sol Friedberg at Brown in Spring 2002 which was in turn party based on Bump's grey book. Other references are a number of Jacquet's papers, JPSS's works, and Cogdell's notes from Trieste and Park City. Email
Tengely, Szabolcs
Leiden University. Diophantine equations, Magma software.
Number Theory, Linux Distributions, Chess Moved
Toplic, Manfred
Computational number theory, prime numbers.
Manfred Toplic' s Homepage Manfred Toplic Klagenfurt , Austria Eastern Longitude: 14 19' 03" Northern Latitude: 46 36' 50" 440 meters ASL Astronomy and Mathematics I am a amateur number theorist and amateur astronomer and member of the Astronomical Society of Carinthia And here is a page of one of my other hobbies: Oldtimer cars My discovery of NINE AND TEN CONSECUTIVE PRIMES IN ARITHMETIC PROGRESSION (The amazing story of the discovery of nine and finally ten CP in AP) With Yves Gallot 's program Proth.exe (named after Francois Proth ) I am searching for Proth Primes (Primes of the form: k * 2n + 1) , Woodall Primes (Primes of the form: n * 2n - 1 ) and for Generalized Fermat Primes (Primes of the form: bN + 1 , with b even and N=2n). The largest I found so far is 5*2^1320487 + 1 (397507 digits) At the time of the discovery (March 15, 2002) this was the largest known Proth-Prime and the 7th largest known prime. Other large Proth Primes I found: 5*2^1282755 + 1 (386148 digits) 5*2^819739 + 1 (246766 digits) On September 25, 2000 I found the world's largest known Woodall Prime: 667071*2^667071 - 1 (200815 digits) References: Chris Caldwell's The top twenty - WOODALL Primes , Another Prime page by Chris K. Caldwell Yves Gallot's page The Chronology of Prime Number Records On 1999 April, 23 10 Palindromic Primes in Arithmetic Progression have been found. (Here I was a member of the search team.) References: Patrick DeGeest's page Palindromic Primes , 1999 May On 1999 September, 28 8 Primes in *quadratic* Progression have been found. (A sequence of seven Pythagorean triangles, where (i) the lengths of the hypotenuse and one leg of each triangle are primes, and (ii) the hypotenuse is the shorter leg of the next triangle in the chain.) (Here I was also a member of the search team.) With Tony Forbes program MFAC.EXE I was searching for a factor of MM61, the Double-Mersenne Number 2^(2^61 - 1) - 1. Some years ago I participated in Paul Zimmermann' s ECMNET I tried to factorize some of the so-called Cunningham composites with ECM (Elliptic curve method). I also participated in GIMPS (Great Internet Mersenne Prime Search) There are lots of unused (idle) cpu cycles to spare, and I'm investing them in science ! Math Pages Astronomy Pages Last updated on 2005 August 04, by Manfred Toplic
Tucker, Thomas J.
University of Georgia. Diophantine geometry. Auctex for Windows.
Thomas Tucker's Home Page Thomas J. Tucker Voice: Phone Number: (706)-542-2575 Email address: ttucker@math.uga.edu Office Number: 523A Boyd Postal Address: Department of Mathematics University of Georgia Athens, GA 30602 My CV in postscript form My CV in pdf form My CV in dvi form My Resum in HTML form Publications Thue equations and the method of Chabauty-Coleman (joint with D. Lorenzini). Inventiones Mathematicae 148 (2002), 47-77; This is available as a postscript file , as a pdf file , or as a dvi file Irreducibility, Brill-Noether loci, and Vojta's inequality (with an appendix by Olivier Debarre). Transactions of the AMS , to appear. This is available as a postscript file , as a pdf file , or as a dvi file. (Appendix: as a postscript file , as a pdf file , or as a dvi file.) The number of fields generated by the square root of values of a given polynomial (joint with P. Cutter and A. Granville). Canadian Mathematical Bulletin , to appear. This is available as a postscript file , as a pdf file , or as a dvi file Arithmetic discriminants and morphisms of curves (joint with X. Song), Transactions of the AMS 353 (2001), 1921--1936. Dirichlet's theorem, Vojta's inequality, and Vojta's conjecture (joint with X. Song). Compositio Mathematica 116 (1999), 219--238. How Hamiltonian can a finite group be? (joint with J. Sherman and M. E. Walker) Archiv der Mathematik (Basel) 357 (1991), 1--5. Preprints Exceptional covers and bijections of rational points (joint with M. Zieve). Preprint. This is available as a postscript file , as a pdf file , or as a dvi file Moving targets for points of bounded degree on curves. Preprint. This is available as a postscript file , as a pdf file , or as a dvi file. Teaching Math 8430 Fall 2000 Math 2200 Spring 2001 Auctex for Windows Auctex provides a nice environment for using tex and latex. Here is a page that provides information on installing it in Windows (thanks to Dave Vanness at the University of Wisconsin) Instructions for Installing Auctex in Windows There is one change you should make to the instructions found there: use the following tex-site.el file in place fo the tex-site.el found at the site above, since it provides support for tex, amstex, pdftex, pdflatex, and ghostview tex-site.el My Stuff Travel
Tsfasman, Michael
Institute for Information Transmission Problems, Russian Academy of Sciences. Algebraic geometry in relation to number theory (varieties over non-algebraically closed fields, especially over finite fields and number fields, parallelism between the function field and number field case, curves, rational varieties, rational points and zero-cycles, elliptic curves and abelian varieties, towers of varieties and asymptotic theory); Number theory (global fields, zeta-functions); Error-correcting codes; Lattices and sphere packings
Michael TSFASMAN Updated: January 1999 Prof. Dr. Michael A. T s f a s m a n Michael A. Tsfasman Dobrushin Mathematics Laboratory, Institute for Information Transmission Problems, Russian Academy of Sciences, 19 Bolshoi Karetny, 101447 Moscow GSP-4, RUSSIA Telephone: (+7-095)-935-2872 Fax: (+7-095)-209-0579 E-mail: tsfasman@iitp.ru Curriculum Vitae Books and research papers Family Russian page Institute for Information Transmission Problems (IPPI) Independent University of Moscow There were visits on this homepage.
Tschinkel, Yuri
University of Illinois at Chicago. Algebraic geometry, number theory and harmonic analysis.
Yuri Tschinkel Yuri Tschinkel's Home Page CV Research
Trifonov, Ognian
University of South Carolina. Analytic number theory and approximation theory; lattice points close to a curve or surface; applications to gap problems.
USC, Department of Mathematics, Ognian Trifonov Ognian Trifonov (Ph.D., Sofia University, 1989), Analytic Number Theory and Approximation Theory with particular interests in the use of finite differences to determine information about lattice points close to a curve or surface. Interests also include the application of these results to gap problems in Number Theory. E-mail: trifonov@math.sc.edu Mail: Ognian Trifonov Department of Mathematics University of South Carolina Columbia, SC 29208 USA Telephone: (803) 777-3882 FAX: (803) 777-3783
Thakur, Dinesh S.
University of Arizona. Number theory and arithmetic geometry.
Dinesh S. Thakur Dinesh S. Thakur's Home Page Will be updated occasionally with new information PAGE FORMAT LAST MODIFIED: May 2004. Departmental homepage cv.dvi cv.pdf publicationlist.dvi publicationlist.pdf abstracts.dvi abstracts.pdf updates.dvi updates.pdf Book: Function Field Arithmetic Book: Cyclotomic Fields and Related topics Papers: Will send these by mail email on request. Warning: The email versions may not be exactly the same as the published versions. In particular, page numbers etc. will be wrong, so that email versions should not be used for the reference. For misprints etc. see update file. How to contact me: E-mail: thakur (at sign) math.arizona.edu (Will always work) Arizona Phone: (520)-621-2416(office), 621-3351(messages), 621-8322 (fax) Arizona Mail: Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA
Top, Jaap
University of Groningen. Arithmetic algebraic geometry.
J.Top Department of Mathematics and Computing Science Staff J. Top Affiliation Professional biography Onderwijs Research Pi in de Pieterskerk Affiliation Dr. J. Top University of Groningen, Department of Mathematics P.O. Box 800, 9700 AV Groningen, The Netherlands Tel: +31 (0)50 3633986 Fax: +31 (0)50 3633800 E-mail: J.Top@math.rug.nl Professional biography Onderwijs Lineaire Algebra 1 MRI Master Class course Elliptic Curves Aspects of Algebra Postscript files van een aantal dictaten kan je hier downloaden. Dat zijn: Differentiaal- en integraalrekening (met Henk de Snoo) Lijnen, vlakken en uilen Kwadrieken Algebra 1 (groepen) Algebra (ringen, lichamen, modulen; dit is een bewerking van het dictaat van Oort, Lenstra en Van Geemen) Dynkin diagrammen wortelsystemen Coderingstheorie Algebra en Meetkunde Local fields Algebra en Computers Galois theory Riemann surfaces (dictaat van M. van der Put) Research Other information . Speeltuin van de wiskunde , edited by Bart de Smit and Jaap Top. Comments via J. Top Last update: April 18, 2004
Thunder, Jeff
Northern Illinois University. Geometry of numbers.
Home Page for Jeff Thunder Jeff Thunder Hi. I'm new at this WWW stuff, so please be gentle! I can be contacted by email, phone or usual mail. jthunder@math.niu.edu (815) 753-6712 Dept. of Math., NIU, DeKalb, IL 60115 Click here to access mathematical papers. I don't have a picture here, but if you are sufficiently perverted, you can find all sorts of them on the naughtier newsgroups. None are of me, I might add. This homepage first erected March 23, 1995 (Revised Oct. 11, 1995) jthunder@math.niu.edu FYEO
Tichy, Robert F.
Technische Universitt Graz. Uniform distribution and discrepancy; Diophantine equations; asymptotic analysis; algorithmic number theory; fractal structures in number theory; stochastic analysis; information-based complexity; quasi-Monte Carlo methods; mathematics in finance.
Robert F. Tichy Robert F. Tichy's Homepage List of current courses and lectures Office: +43 316 873 7120 Fax: +43 316 873 7126 email: tichy@tugraz.at my address: Institut fr Mathematik A Technische Universitt Graz Steyrergasse 30 A-8010 Graz Austria Research Interests Uniform Distribution and Discrepancy Diophantine Equations Asymptotic Analysis Algorithmic Number Theory Fractal Structures in Number Theory Stochastic Analysis Information Based Complexity Quasi-Monte Carlo Methods Mathematics in Finance and Insurance Administrative Positions Head of the Department of Mathematics (TU Graz, 1994-2000) Co-Speaker of the research area "Number-Theoretic Algorithms and their Applications" (funded by FWF) Member of the Senate of the TU Graz (1998- ) Member of the Convent of the TU Graz(2003-2004) Vice-President of the Austrian Mathematical Society (OeMG) (2002- ) Dean (Faculty of Science, TU Graz, 2003), Dean of the Faculty of Mathematical and Physical Sciences (2004- ) Editorial Duties Journal of Number Theory (1991 - 2000) Journal de Thorie des Nombres, Bordeaux Monatshefte fr Mathematik (advisory board) Mathematica Slovaca Fibonacci Quarterly Grazer Mathematische Berichte "Number Theoretic Analysis", Lecture Notes in Mathematics volume 1452, Springer 1990, with E. Hlawka "Algebraic Number Theory and Diophantine Analysis" , de Gruyter Proceedings in Mathematics, de Gruyter 2000, with F. Halter-Koch Professional Positions and Awards Ph.D. University of Vienna (1979) Life-Insurance consultant (1979-1981) Assistant (Vienna, 1980-1983) Lecturer on Actuarial Sciences (Linz, 1980) Award of the Austrian Mathematical Society (1985) Dozent (TU Vienna, 1983-1990) Full Professor (TU Graz, since 1990) Visiting Positions: Salzburg (1986), Tata Institute Bombay (1992), Marseille (1993, 1995), Debrecen (1997), University of Illinois (Urbana-Champaign, 2000) Member of the New York Academy of Sciences (1997-2002) Corresponding Member of the Austrian Academy of Sciences (2004- ) Selected Publications Simulation methods in ruin models with non-linear dividend barriers, Math. Comp. Sim. 62 (2003), 277-287, with H. Albrecher und R. Kainhofer Perfect powers in linear recurring sequences, Acta Arith., 107.1 (2003), 9-25, with C. Fuchs Thomas' family of Thue equations over imaginary quadratic fields, J. Symbolic Comput., 34 (2002), 437-449, with C. Heuberger und A. Peth On the diophantine equation Gn(x)=Gm(P(x)), Monatsh. Math. 137 (2002), 173 - 196, with C. Fuchs und A. Peth Diophantine Equations and Bernoulli Polynomials (with an appendix by A. Schinzel), Compositio Mathematica 131 (2002), 173-188, with Y. Bilu, B. Brindza, P. Kirschenhofer and A. Pintr A Model in Ruin Theory using Derivative Securities, Mitt. der Vereinigung Schweizer Versicherungsmath. 1 (2002), with T. Siegl Combinatorial and Arithmetical Properties of Linear Numeration Systems, Combinatorica 22 (2002), 245 - 267, with P.J. Grabner and P. Kirschenhofer Metric Theorems for Distribution Measures of Pseudorandom Sequences, Monatsh. Math. 135 (2002), 321 - 326, with W. Philipp On a Gamma Series Expansion for the Time-Dependent Probability of Collective Ruin, Insurance: Mathematics Economics 29 (2001), 345 - 355, with H. Albrecher und J.L. Teugels Fractal Properties of Number Systems, Periodica Math. Hung. 40 (2001), 51 - 68, with W. Mller und J. Thuswaldner Diophantine Equations for Second Order Recursive Sequences of Polynomials, Quarterly J. Oxford, 53 (2001), 161 - 169, with A. Dujella Pair correlations and U-statistics for independent and weakly dependent random variables, Illinois J. Math. vol. 45, nr. 2, (2001), 559-580, with I. Berkes and W. Philipp Zur Konvergenz eines Lsungsverfahrens fr ein Risikomodell mit gammaverteilten Schden, Mitt. Schweiz. Aktuarvereinigung, 2 (2000), 115-128, with H. Albrecher Octahedrons with equally many lattice points, Periodica Math. Hung., 40 (2000), 229-238, with Y.F. Bilu and Th. Stoll An Erds-Kac theorem for systems of q-additive functions, Indag. Mathem., N.S., 11 (2000), 283-291, with J.M. Thuswaldner The Diophantine equation f(x) = g(y), Acta Arith., 95 (2000), 261-288, with Y.F. Bilu Ruin theory with risk proportional to the free reserve and securitization, Insurance Mathematics Economics, 26 (2000), 59-73, with Th. Siegl Effective solution of families of Thue equations containing several parameters, Acta Arith., 91 (1999), 147-163, with C. Heuberger A process with stochastic claim frequency and a linear dividend barrier, Insurance: Mathematics and Economics 24 (1999), 51-65, with T. Siegl Thue Equations associated with Ankeny-Brauer-Chowla Number Fields, Journal London Math. Soc. (2) 60 (1999), 1-20, with F. Halter-Koch, G. Lettl, A. Peth. Asymptotic analysis of a subclass of functional equations, Aequationes Math. vol. 55 (1998), 1 2, 91-105, Birkhuser with G. Derfel, J.M. Thuswaldner and F. Vogel, Equidistribution and Brownian Motion on the Sierpinski Gasket, Monatsh. Math. 125 (1998) 147-164, with P. Grabner. Sequences, Discrepancies and Applications, Lecture Notes in Mathematics, vol. 1651, Springer (1997) , with M. Drmota. Lsungsverfahren eines Risikomodelles bei exponentiell fallender Schadensverteilung, Mitt. der Vereinigung Schweizer Versicherungsmath. 1 (1996) 95-118, with T. Siegl. Quasi-Monte-Carlo Methods and the Dispersion of Point Sequences, Journal for Mathematical and Computer Modeling, 23 (1996), 9-23 with G. Rothe. Odometers and systems of numeration, Acta Arith., 70 (1995), 103-123, with P.Grabner und P.Liardet. Spherical Designs, Discrepancy and Numerical Integration, Math. Comp. Vol. 60 201 (1993), 327-336, with P. Grabner. Uniform Distribution Preserving Maps, Acta Arith. 60 (1991), 177-189, with R. Winkler. Deviations from uniformity in random strings, Probability Th. and Rel. Fields, 80 (1988), 139-150, with P. Flajolet and P. Kirschenhofer. Ein metrischer Satz ber vollstndig gleichverteilte Folgen, Acta Arith. 48 (1987), 197-207. My Family Philipp und Sophie im Gebirge: Philipp und Sophie beim Schifahren: February 2004: Carneval 2004: Hiking and mountain climbing: You might also like to have a look at some more photographs taken at regular mountain tours. Also, look at some pictures from South Africa (2003) Back to the homepage of the group
Tijdeman, Robert
Leiden University. Diophantine analysis, analytic number theory.
Robert Tijdeman
Taya, Hisao
Tohoku University. Algebraic number theory, Iwasawa theory.
Hisao TAYA -Math. Lab. GSIS Tohoku Univ.- English Division of Mathematics, Graduate School of Information Sciences, Tohoku University [ English | Japanese ] Welcome to HISAO TAYA's Home Page !! 1. Research Interest 2. List of Papers 3. My Vita Home Page of Div. of Math., GSIS, Tohoku University Home Page of Graduate School of Information Sciences, Tohoku University Home Page of Tohoku University Home Page of Mathematical Institute, Tohoku University Graduate School of Information Sciences, Tohoku University, Aramaki-Aza-Aoba 09, Aoba-ku, Sendai 980-8579, JAPAN TEL:+081-22-795-4638, FAX:+081-22-795-4654 Hisao TAYA
Tan, Victor
National University of Singapore. Automorphic forms and representations, algebraic number theory, modular forms and elliptic functions, combinatorial designs and difference sets.
Tan Victor Home Page of Tan Victor Education B.Sc.(Hons), M.Sc., National University of Singapore Ph.D., University of California, Los Angeles Current interests Linear Preserver Problems Number Theory Automorphic Forms Combinatorial Designs List of publications The module I am teaching this semester Singapore Mathematical Society Enrichment Programme Script writing for stage plays Great mathematicians Some mathematical links Tan Victor Block S14 02-17 Department of Mathematics National University of Singapore 2 Science Drive 2, Singapore 117543 Republic of Singapore Send me an email at: mattanv@nus.edu.sg (65) 6516-7936 (office) (65) 6779-5452 (fax) Back to the home page of the Department of Mathematics
Taylor, Martin
UMIST. Algebraic number theory, Galois module structure.
Mathematics Staff Homepage Martin Taylor Professor in Pure Mathematics EPSRC Senior Research Fellow Royal Society Wolfson Research Fellow Qualifications: M.A. (Oxford), Ph.D (London). Room No. O15 Administrative duties: Member of EPSRC College, Chairman of Royal Society Scientific Unions Committee Research: Galois, Hermitian and quadratic structure for arithmetic varieties. Publications List CV Other activities: Flyfishing, Hill walking. Professor M J Taylor FRS Mathematics Department, UMIST P.O. Box 88 Manchester M60 1QD UK (0161) 200 3640 (use + 44 161 200 3640 from overseas) Fax: (0161) 200 3669 Email: Martin.Taylor@umist.ac.uk
Teske, Edlyn
University of Waterloo. Computational number theory, cryptography.
CACR: People: Faculty: Edlyn Teske Edlyn Teske Assistant Professor Address: Department of Combinatorics and Optimization University of Waterloo Waterloo, Ontario, Canada, N2L 3G1 Phone: (519) 888-4567 x3473 Fax: (519) 725-5441 Email: eteske at uwaterloo.ca Office: MC 4030 Research Interests: Cryptography. Public-key cryptosystems. Discrete logarithm problem. Elliptic and hyperelliptic curves. Algebraic number theory computations. Quadratic number fields. Generic algorithms for finite abelian groups. Random walks in finite sets. Algebraic complexity theory. Degrees Publications Conferences Teaching Students Links Edlyn Teske
Taylor, Richard
Harvard. Arithmetic algebraic geometry, automorphic forms. Preprints.
Richard Taylor's Home Page RICHARD TAYLOR Here are some recent papers. They are available either as dvi or as postscript files. They may be very slightly different from the published versions, e.g. they may not include corrections made to the proofs. Ihara's lemma and potential automorphy. M.Harris, N.Shepherd-Barron and R.Taylor preprint. dvi Postscript Automorphy for some l-adic lifts of automorphic mod l representations. L.Clozel, M.Harris and R.Taylor preprint. dvi Postscript Compatibility of local and global Langlands correspondences. R.Taylor and T.Yoshida preprint. dvi Postscript Galois representations. (Review article.) R.Taylor Proceedings of ICM 2002, volume I, 449-474. dvi Postscript Galois representations. (Long version of above review article.) R.Taylor Annales de la Faculte des Sciences de Toulouse 13 (2004), 73-119. dvi Postscript Galois representations. R.Taylor slides for talk at ICM 2002. dvi Postscript On the meromorphic continuation of degree two L-functions. R.Taylor preprint. dvi Postscript Remarks on a conjecture of Fontaine and Mazur. R.Taylor Journal of the Institute of Mathematics of Jussieu 1 (2002), 1-19. dvi Postscript On icosahedral Artin representations. II R.Taylor American Journal of Mathematics 125 (2003), 549-566. dvi Postscript On the modularity of elliptic curves over Q. C.Breuil, B.Conrad, F.Diamond and R.Taylor J.A.M.S. 14 (2001), 843-939. dvi Postscript On icosahedral Artin representations. K.Buzzard, M.Dickinson, N.Shepherd-Barron and R.Taylor Duke Math. J. 109 (2001), 283-318. dvi Postscript The geometry and cohomology of some simple Shimura varieties. M.Harris and R.Taylor Annals of Math. Studies 151, PUP 2001. Modularity of certain potentially Barsotti-Tate Galois representations. B.Conrad, F.Diamond and R.Taylor J.A.M.S. 12 (1999) 521-567. dvi Postscript Companion forms and weight one forms. K.Buzzard and R.Taylor Annals of Mathematics 149 (1999), 905-919. dvi Postscript Icosahedral Galois representations R.Taylor Pacific Journal of Math., Olga Taussky-Todd memorial issue (1997) 337-347 dvi Postscript Mod 2 and mod 5 icosahedral representations. N.Shepherd-Barron and R.Taylor J.A.M.S. 10 (1997) 283-298. dvi Postscript Ring theoretic properties of certain Hecke algebras. R.Taylor and A.Wiles Annals of Math. 141 (1995) 553-572. dvi Postscript On congruences between modular forms. R.Taylor PhD. thesis, Princeton University 1988. dvi Postscript Richard Taylor rtaylor@math.harvard.edu
Sohn, Jaebum
Yonsei University, Seoul. Classical number theory and special functions.
My Webpage Jaebum Sohn Assistant Professor Office: 249 Science Bldg. Phone: (02) 2123-2599 Fax: (02) 392-6634 Email: jsohn@yonsei.ac.kr Education: Ph.D., University of Illinois at Urbana-Champaign (Advisor: Dr. Bruce C. Berndt) M. S., B. S., Yonsei University, Seoul, Korea Research: My research interests are in the areas of classical number theory and special functions, specially in : Continued Fractions; Modular Equations; Theta Elliptic Functions; Ramanujan's Notebooks; q-series; and (Basic) Hypergeometric Functions. Teaching 2005 2 ( ) Fall 2005 Engineering Mathematics(2) (Course No: MAT1012-03) Mathematical Links: American Mathematical Society Korean Mathematical Society Last update on August 30, 2005. This page is maintained by Jaebum Sohn. ( jsohn@yonsei.ac.kr )
Stewart, Cameron L.
University of Waterloo. Number theory. Publications, preprints, lecture notes.
Cameron L. Stewart - Homepage UWdir Math Google Search Math Index Search Skip to the content of the web site. Math Home About Math Depts Schools Programs Grad Research Studies Current Students Prospective Students Alumni Friends Services Facilities UW Home Cameron L. Stewart University Professor Canada Research Chair in Number Theory Department of Pure Mathematics University of Waterloo Waterloo, Ontario, Canada N2L 3G1 Office room number: MC 5051 Office telephone number: 519-888-4567 ext. 5567 Fax number: 519-725-0160 Curriculum Vitae Publications In refereed journals and books In refereed conference proceedings In seminar proceedings Course Notes (in pdf format) PMath 440 640 Analytic Number Theory (prepared by Stephen Forrest) (updated August, 2005) PMath 441 641 Algebraic Number Theory (prepared by Stephen Forrest) Linear Forms in Logarithms and Diophantine Equations (prepared by Dan Wolczuk) Photos 90th Convocation - Faculty of Mathematics, Waterloo, June 2005 2003 Ostrowski Prize Presentation, Waterloo, September 2004 Canadian Embassy Reception honouring Fields Medallists and Nevanlinna Prize Winner - Beijing, August 2002 Canada Research Chair Program Department of Pure Mathematics Faculty of Mathematics University of Waterloo 200 University Avenue West Waterloo, Ontario, Canada N2L 3G1 519 888 4567 ext. 3484 contact us | | http: www.math.uwaterloo.ca PM_Dept Last Modified: Tuesday 27 September 2005
Sairaiji, Fumio
Hiroshima International University. Formal groups, Q-curves. Publications.
Homepage of Fumio SAIRAIJI For Students Fumio SAIRAIJI Department of Integrated Architecture Faculty of Infrastructural Technologies Hiroshima International University 5-1-1, Hiro-Koshingai, Kure-city, Hiroshima 737-0112, Japan Hiro, Hiroshima 737-0112, Japan e-mail: sairaiji@it.hirokoku-u.ac.jp Papers: On congruences between the coefficients of two L-series which are related to a hyperelliptic curve over Q, Osaka J. Math. 37 (2000), 789-799. A note on Ono's numbers associated to imaginary quadratic fields (joint work with Kenichi Shimizu), Proc. Japan Acad., 77, Ser A (2001), 29-31. Formal groups of certain Q-curves over quadratic fields, Osaka J. Math. 39 (2002), 223-243. An inequality between class numbers and Ono's numbers associated to imaginary quadratic fields (joint work with Kenichi Shimizu), Proc. Japan Acad., 78, Ser. A (2002), 105-108. Formal groups of building blocks over finite abelian extensions of Q, to appear in Bull. London Math. Soc. Proceedings: On congruences between the coefficients of two L-series which are related to a hyperelliptic curve over Q, Waseda Univ. Proc. of Sympos. on Number Theory, (1997), 87-91. On Honda theory of formal groups of certain Q-curves over quadratic fields, Proc. of 4th. Sympos. on Number Theory at Tsudajyuku Univ., (1999), 32-40. On Honda theory of formal groups of certain Q-curves over quadratic fields, RIMS Kokyuroku 1097 (1999), 144-150. An inequality between class numbers and Ono's numbers associated to imaginary quadratic fields (joint work with Kenichi Shimizu), Waseda Univ. Proc. of Sympos. on Number Theory, (2002), 95-102. On some generalizations of Honda theory of formal groups of elliptic curves, "Cryptography and algebraic curves" 3rd workshop, (2002), 105-115. Formal groups of building blocks over finite abelian extensions of Q, RIMS Kokyuroku 1376 (2004), 171-180. Lectures: Basic Mathematics 1 Basic Mathematics 2 Applied Mathematics 1 (Linear algebra etc.) Applied Mathematics 2 (Differential equations etc.) Statistics Part-time lectures: Hiroshima University(2003) Chuo University(2004)
Szalay, Lszl
University of West Hungary. Diophantine equations.
Welcome to Lszl Szalay's Home Page Dr. Lszl Szalay head of Department of Mathematics Institute of Mathematics, Statistics and Informatics Faculty of Economy University of West Hungary H-9400 Sopron, Erzsbet u. 9. Tel: (36) 99 518-423 Fax: (36) 99 518-423 e-mail: laszalay@ktk.nyme.hu Last modified: 26. April 2005. If You have any comments or notice on the page, please take up contact with Gbor Patonai .
Shorey, T. N.
Tata Institute for Fundamental Research. Transcendence, Diophantine equations. Publications.
Welcome To T. N. Shorey's Home Page T.N. Shorey's Home Page Here is my list of publications in DVI format. You can read about my work in the article 115. Here is the list of my papers; clicking the number will give you the paper(if available) in DVI or PS format: Book (with R. Tijdeman) Exponential Diophantine equations, Cambridge Tracts in Mathematics 87 (1986), Cambridge University Press. 115 Diophantine approximations, Diophantine equations, Transcendence and Applications, Indian Jour. of Pure and Applied Math, to appear. 114 Some topics in Prime number theory , Bulletin of Bombay Math. Colloquium, to appear. 113 (with Shanta Laishram ) Grimm's Conjecture on consecutive integers, to appear. 112 (with Shanta Laishram ) The greatest prime divisor of a product of terms in an arithmetic progression, Indag. Math, to appear. 111 (with Shanta Laishram ) The greatest prime divisor of a product of consecutive integers, Acta Arith., to appear. 110 Powers in arithmetic progress (III) , Ramanujan Math. Society Publication, to appear. 109 (with N. Saradha) On the equation n(n+d) ... (n+(i-1)d)(n+(i+1)d) ... (n+(k-1)d) = y^l with 0 i k-1 , Acta Arith., to appear. 108 (with F. Luca) Diophantine equations with products of consecutive terms in Lucas sequences, Journal of Number Theory, 114 (2005), 541-560. 107 (with Shanta Laishram ) Number of prime divisors in a product of terms of an arithmetic progression, Indag. Math., 15 (2004), 505-521. 106 (Anirban Mukhopadhyay) Almost squares in arithmetic progression (III), Indag. Math., 15 (2004), 523-533. 105 (with N. Saradha) Contributions towards a conjecture of Erdos on perfect powers in arithmetic progressions, Compositio Math., 141 (2005), 541-560. 104 (with Shanta Laishram ) Number of prime divisors in a product of consecutive integers, Acta Arith. 113 (2004), 327-341. 103 Approximations of algebraic numbers by rationals: A theorem of Thue, Proceedings of a workshop held at HRI, Allahabad on Elliptic Curves in 2000, to appear. 102 The generalised Ramanujan-Nagell equation, Applicable Mathematics in the Golden Age, edited by J.C. Mishra, Narosa (2003), 490-495. 101 (with Anirban Mukhopadhyay) Square free part of products of consecutive integers, Publ. Math. Debrecen, 64 (2004), 79-99. 100 (Anirban Mukhopadhyay) Almost squares in arithmetic progression (II), Acta Arith., (2003), 1-14. 99 (with Y. Bugeaud) On an equation of Goomaghtigh II, Pacific Jour. Math. 207 (2002), 61-76. 98 (with N. Saradha) Almost squares and factorisations in consecutive integers, Compositio Math. 138 (2003), 113-124. 97 (with N. Saradha) Almost squares in arithmetic progression, Compositio Math., 138 (2003), 73-111. 96 Powers in arithmetic progression (II), Analytic Number Theory, RIMS Kokyuroku (2002), Kyoto University, to appear. 95 Powers in arithmetic progression, A Panorama in Number Theory or The View from Baker's Garden, edited by G.Wustholz, Cambridge University Press (2002), 341-353. 94 An equation of Goormaghtigh and diophantine approximations, Current Trends in Number Theory, edited by S.D.Adhikari, S.A.Katre and B.Ramakrishnan, Hindustan Book Agency, New Delhi (2002), 185-197. 93 (with N. Saradha and R. Tijdeman) Some extensions and refinements of a theorem of Sylvester, Acta Arith. 102 (2002), 167-181. 92 (with Y. Bugeaud), On the number of solutions of the generalised Ramanujan-Nagell equation, Jour. Reine Angew. Math. 539 (2001), 55-74. 91 Mathematical Contributions, Bulletin Bombay Mathematical Colloquium 15 (1999) published in 2001, 1-19. 90 (with S. D. Adhikari, N. Saradha and R. Tijdeman) Transcendental Infinite Sums, Indag. Math. N.S. 12 (2001), 1-14. 89 (with G. Hanrot and N. Saradha) Almost perfect powers in consecutive integers, Acta Arith. 99 (2001), 13-25. 88 (with N. Saradha) Almost perfect powers in arithmetic progression, Acta Arith. 99 (2001), 363-388. 87 Some conjectures in the theory of exponential diophantine equations, Publicationes Math. Debrecen 56 (2000), 631-641. 86 (with Y. Bugeaud, M. Mignotte and Y. Roy) The equation $\frac{x^n-1}{x-1} = y^q$ has no solution with $x$ square, Math. Proc. Camb. Phil. Soc. 127 (1999), 353-372. 85 (with N. Saradha) The equation $\frac{x^n-1}{x-1} = y^q$ with $x$ square, Math. Proc. Camb. Phil. Soc. 125 (1999), 1-19. 84 (with F. Beukers and R. Tijdeman) Irreducibility of polynomials and arithmetic progressions with equal products of terms, Number Theory in Progress, Volume 1 (1999), Walter de Gruyter, Berlin, 11-26. 83 The equation $a\frac{x^n-1}{x-1} = by^q$ with $ab 1$, Number Theory in Progress, Volume 1 (1999), Walter de Gruyter, Berlin, 473-485. 82 Exponential diophantine equations involving products of consecutive integers and related equations, Number Theory edited by R.P.Bambah, V.C.Dumir and R.J.Hans-Gill, Hindustan Book Agency (1999), 463-495. 81 (with Yu.V. Nesterenko) On an equation of Goormaghtigh, Acta Arith. 83 (1998), 381-389. 80 Integer solutions of exponential diophantine equations, Bulletin of Bombay Mathematical Colloquium 13 (1998), 1-21. 79 (with R. Tijdeman) Irrationality criteria for numbers of Mahler's type, Analytic Number Theory ed. by Y. Motohashi, London Mathematical Society Lecture Note Series 247 (1997), 341-351. 78 (with Noriko Hirata-Kohno) On the equation $(x^m-1) (x-1) = y^q$ with $x$ power, Analytic Number Theory ed. by Y. Motohashi, London Mathematical Society Lecture Note Series 247 (1997), 119-125. 77 (with R. Balasubramanian) Perfect powers in products of terms in an arithmetical progression (IV), Number Theory, Contemporary Mathematics 210 (1997), 257-263, American Mathematical Society. 76 (with R.Tijdeman) Some methods of Erd\"{o}s applied to finite arithmetic progressions, The Mathematics of Paul Erd\"os, ed. by Ronald L. Graham and Jaroslav Ne\v{s}et\v{r}il, Springer (1997), 251-267. 75 (with R. Balasubramanian, M. Langevin, and M. Waldschmidt) On the maximal length of two sequences of integers in arithmetic progressions with the same prime divisors, Monatshefte f\"ur Mathematik 121 (1996), 295-307. 74 (with M. Mignotte) The equations $(x+1) \cdots (x+k) = (y+1) \cdots (y+mk), m=5,6$, Indag. Math., N.S. 7 (1996), 215-225. 73 (with Yu.V. Nesterenko) Perfect powers in products of integers from a block of consecutive integers (II), Acta Arith. 76 (1996), 191-198. 72 Some applications of diophantine approximations to diophantine equations, Number Theory, Paris 1993-4, ed. by S. David, London Math. Soc. Lecture Note Series 235 (1996), 189-198. 71 Perfect powers in products of arithmetical progressions with fixed initial term, Indag. Math., N.S. 7 (1996), 521-525. 70 (with N. Saradha and R.Tijdeman) On values of a polynomial at arithmetic progressions with equal products, Acta Arith. 72 (1995), 67-76. Correction 69 (with N. Saradha and R. Tijdeman) On the equation $x (x+1) \cdots (x+k-1) = y(y+d)\cdots (y+(mk-1)d), \ \ m=1, 2,$ Acta Arith. 71 (1995), 181-196. 68 (with N. Saradha and R. Tijdeman) On arithmetic progressions of equal lengths with equal products, Math. Proc. Camb. Phil. Soc. 117 (1995), 193-201. 67 On a conjecture that a product of $k$ consecutive positive integers is never equal to a product of $mk$ consecutive positive integers except for 8.9.10 =6! and related problems, Number Theory, Paris 1992-3, ed. by S. David, London Math. Soc. Lecture Note Series 215 (1995), 231-244. 66 (with N. Saradha and R.Tijdeman) On arithmetic progressions with equal products, Acta Arith. 68 (1994), 89-100. 65 (with N. Saradha) On the equation $x(x+d_1) \cdots (x+(k-1)d_1) = y(y+d_2) \cdots (y+(mk-1)d_2)$, Proc. Indian Acad. Sci. (Math.Sci.) 104 (1994), 1-12. 64 (with R. Balasubramanian) Squares in products from a block of consecutive integers, Acta Arith. 65 (1994), 213-220. 63 Applications of Baker's theory of linear forms in logarithms to exponential diophantine equations, Analytic Number Theory, RIMS Kokyuroku 886 (1994), 48-60, Kyoto University. 62 (with R. Balasubramanian) On the equation $f(x+1) \cdots f(x+k) = f(y+1) \cdots f(y+mk)$, Indag. Math., N.S.4 (1993), 257-267. 61 On the equation $x^{\ell}+y^{\ell}=2z^{\ell}$ and related problems, Seminar on Number Theory, Caen 1992 93, University of Caen, Exp. VI. 60 (with R. Tijdeman) On the greatest prime factor of an arithmetical progression (III), Diophantine Approximation and Transcendental Numbers, Luminy 1990, edited by Ph. Philippon, Walter de Gruyter, New York (1992), 275-280. 59 (with R. Tijdeman) On the number of prime factors of a finite arithmetical progression, Acta Arith. 61 (1992), 375-390. 58 (with R. Tijdeman) Perfect powers in products of terms in an arithmetical progression (III), Acta Arith. 61 (1992), 391-398. 57 (with R. Tijdeman) Perfect powers in products of terms in an arithmetical progression (II), Compositio Math. 82 (1992), 119-136. 56 (with R. Tijdeman) Perfect powers in arithmetical progression (II), Compositio Math. 82 (1992), 107-117. 55 (with N. Saradha) On the equation $x(x+d) \cdots (x+(k-1)d) = y (y+d) \cdots (y+ (mk-1)d)$, Indag. Math., N.S.3 (1992), 237-242. 54 (with N. Saradha) On the equation $(x+1) \cdots (x+k) = (y+1) \cdots (y+mk)$, Indag. Math., N.S.3 (1992), 79-90. 53 (with N. Saradha) The equations $(x+1) \cdots (x+k) = (y+1) \cdots (y+mk)$ with $m=3,4,$ Indag. Math., N.S.2 (1991), 489-510. 52 (with R. Tijdeman) On the greatest prime factor of an arithmetical progression, A Tribute to Paul Erdos, edited by A. Baker, B. Bollobas and A. Hajnal, Cambridge University Press (1990), 385-389. 51 (with K. Gyory and M. Mignotte) On some arithmetical properties of weighted sums of $S-$units, Mathematica Pannonica 1 2 (1990), 25-43. 50 (with R. Tijdeman) On the greatest prime factor of an arithmetical progression (II), Acta Arith. 53 (1990), 499-504. 49 (with N. Saradha) On the ratio of two blocks of consecutive integers, Proc. Indian Acad. Sci. (Math. Sci.) 100 (1990), 107-132. 48 (with R. Tijdeman) Perfect powers in products of terms in an arithmetical progression, Compositio Math. (1990), 307-344. 47 (with R. Balasubramanian and M. Waldschmidt) On the maximal length of two sequences of consecutive integers with the same prime divisors, Acta Mathematica Hungarica 54 (1989), 225-236. 46 (with R. Tijdeman) On the number of prime factors of an arithmetical progression, Jour. Sichuan Univ. 26 (1989), 72-74. 45 Integers with identical digits, Acta Arith. 53 (1989), 81-99. 44 (with R. Tijdeman) Perfect powers in arithmetical progression, Jour. Madras University (Section B) 51 (1988), 173-180. 43 (with K. Gyory) On the denominators of equivalent algebraic numbers, Indag. Math. 50 (1988), 29-41. 42 Some exponential Diophantine equations II, Number Theory and Related Topics ed. by\ S. Raghavan, Tata Institute of Fundamental Research, Bombay (1988), 217-229. 41 Some exponential Diophantine equations, New Advances in Transcendence Theory, ed. by A. Baker, Cambridge University Press (1988), 352-365. 40 (with J.-H. Evertse, K. Gyory and R. Tijdeman) Equal values of binary forms at integral points, Acta Arith. 48 (1987), 379-396. 39 (with Ram Murty and Kumar Murty) Odd values of Ramanujan $\tau-$function, Bull. Soc. Math. France 115 (1987), 391-395. 38 (with C.L. Stewart) Pure powers in recurrence sequences and some related Diophantine equations, Jour. Number Theory 27 (1987), 324-352. 37 (with S. Srinivasan) Metrical results on square free divisors of convergents of continued fractions, Bull. London Math. Soc. 19 (1987), 135-138. 36 Ramanujan and binary recursive sequences, Jour. Indian Math. Soc. 52 (1987), 147-157. 35 Perfect powers in products of integers from a block of consecutive integers, Acta Arith. 49 (1987), 71-79. 34 Integer solutions of some equations, Current Science 55, No.17 (1986), 815-817. 33 On the equation $ax^m-by^n=k$, Indag. Math. 48 (1986), 353-358. 32 On the equation $z^q=(x^n-1) (x-1)$, Indag. Math. 48 (1986), 345-351. 31 Perfect powers in values of certain polynomials at integer points, Math. Proc. Camb. Phil. Soc. 99 (1986), 195-207. 30 (with M. Mignotte and R. Tijdeman) The distance between terms of an algebraic recurrence sequence, Jour. Reine Angew. Math. 349 (1984), 63-76. 29 On the ratio of values of a polynomial, Proc. Indian \ Acad. Sci. (Math.Sci.) 93 (1984), 109-116. 28 On the equation $a(x^m-1) (x-1) = b(y^n -1) (y-1)$ (II), Hardy Ramanujan Jour. 7 (1984), 1-10. 27 Linear forms in members of a binary recursive sequence, Acta Arith. 43 (1984), 317-331. 26 (with C.L. Stewart) On the equation $ax^{2t}+bx^ty+cy^2=d$ and pure powers in recurrence sequences, Math. Scand. 52 (1983), 24-36. 25 Applications of linear forms in logarithms to binary recursive sequences, Seminar on Number Theory, Paris 1981 82, Progr. Math. 38, Birkh$\tilde{a}$user, Boston (1983), 287-301. 24 Divisors of convergents of a continued fraction, Jour. Number Theory 17 (1983), 127-133. 23 On the greatest square free factor of members of a binary recursive sequence, Hardy-Ramanujan Jour. 6 (1983), 23-36. 22 (with J.C. Parnami) Subsequences of binary recursive sequences, Acta Arith. 40 (1982), 193-196. 21 The equation $ax^m+by^m=cx^n+dy^n,$ Acta Arith. 41 (1982), 255-260. 20 (with C.L. Stewart) On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers II, Jour. London Math. Soc. (2) 23 (1981), 17-23. 19 (with R. Balasubramanian) On the equation $a(x^m-1) (x - 1)=b(y^n-1) (y-1)$, Math. Scand. 46 (1980), 177-182. 18 On the greatest prime factor of $ax^m +by^n$, Acta Arith. 36 (1980), 21-25. 17 (with A.J. van der Poorten, R. Tijdeman and A. Schinzel) Applications of the Gel'fond-Baker method to Diophantine equations, Transcendence Theory: Advances and Applications, ed. by A. Baker and D.W. Masser, Academic Press, London (1977), 59-77. 16 (with K. Ramachandra and R. Tijdeman) On Grimm's problem relating to factorisation of a block of consecutive integers II, Jour. Reine \ Angew. Math. 288 (1976), 192-201. 15 (with R. Tijdeman) New applications of Diophantine approximations to Diophantine equations, Math. Scand. 39 (1976), 5-18. 14 (with R. Tijdeman) On the greatest prime factors of polynomials at integer points, Compositio \ Math. 33 (1976), 187-195. 13 (with P. Erd\"{o}s) On the greatest prime factor of $2^p-1$ and other expressions, Acta Arith. 30 (1976), 257-265. 12 On linear forms in the logarithms of algebraic numbers, Acta Arith. 30 (1976), 27-42. 11 Some applications of linear forms in logarithms, Seminar Delange-Pisot-Poitou 1975 76, Paris, Exp. 28. 10 Some applications of linear forms in logarithms, Seminar Delange - Pisot Poitou 1975 76, Paris, Exp.3. 9 (with K.Ramachandra and R. Tijdeman) On Grimm's problem relating to factorisation of a block of consecutive integers, Jour. Reine Angew. Math. 273 (1975), 109-124. 8 On the sum ${\displaystyle{\sum_{k=1}^{3}}} \mid 2^{\pi^k} -\alpha_k \mid, \alpha_k$ algebraic numbers, Jour. Number Theory 6 (1974), 248-260. 7 Linear forms in the logarithms of algebraic numbers with small coefficients II, Jour. Indian Math. Soc. 38 (1974), 285-292. 6 Linear forms in the logarithms of algebraic numbers with small coefficients I, Jour. Indian Math. Soc. 38 (1974), 271-284. 5 On gaps between numbers with a large prime factor II, Acta Arith. 25 (1974), 365-373. 4 (with K. Ramachandra) On gaps between numbers with a large prime factor, Acta Arith. 24 (1973), 99-111. 3 $P-$adic analogue of a theorem of Tijdeman and its applications, Indag. Math. 34 (1972), 436-442. 2 Algebraic independence of certain numbers in the $P-$adic domain, Indag. Math. 34 (1972), 423-435. 1 On a theorem of Ramachandra, Acta Arith. 20 (1972), 215-221. Google Number Theory Web School of Mathematics Email School of Mathematics Home Page
Schmidt, Alexander
Universitt Regensburg. Algebraic Number Theory, Higher dimensional class field theory, Iwasawa-theory; Algebraic Geometry, A1-homotopy theory, Motivic (co)homology. Publications.
Alexander Schmidt Alexander Schmidt's Home Page Prof. Dr. Alexander Schmidt NWF I - Mathematik Universitt Regensburg D-93040 Regensburg Germany Zimmer: 232 Telefon: +49-(0)941-943-2781 Fax: +49-(0)941-943-1736 Email: PGP: public key Secretary Collaborators Publications Teaching (in German) Deutschsprachige Seite Research Group "Algebraic Cycles and L-Functions" Workshop on Cobordism: Feb 16-18, 2005 in Regensburg (Schedule) by Alexander Schmidt Stand: 23.9.2005
Siksek, Samir
Sultan Qaboos University. Elliptic curves, Diophantine equations, the Hasse principle. Publications.
Samir Siksek - Department of Mathematics and Statistics Department of Mathematics College of Science Sultan Qaboos University Samir Siksek Assistant Professor Education: B.A. Mathematics, Oxford University, 1990. Certificate of Advanced Study in Mathematics, Cambridge University, 1991. Ph.D. Mathematics, University of Exeter, 1995. Research Area: Number Theory. In particular, I work on elliptic curves, Diophantine equations, the Hasse principle. Selected Publications: Descents on curves of genus 1, Ph.D. thesis, University of Exeter, 1995. Infinite descent on elliptic curves, Rocky Mountain Journal of Mathematics 25 (1995), 1501-1538. (with J. Merriman and N. Smart) Explicit 4-descents on an elliptic curve, Acta Arithmetica LXXVII.4 (1996), 358-404. (with N. Smart) On the complexity of computing the 2-Selmer group of an elliptic curve, Glasgow Mathematical Journal 39 (1997), 251-258. (with N. Smart) A fast Diffie-Hellman protocol in genus 2, Journal of Cryptology 12 (1999), 43-48. The Height Pairing on an elliptic curve with complex multiplication, Arab Journal of Mathematical Sciences 5 (1999), 43-48. Sieving for rational points on hyperelliptic curves, Mathematics of Computation 70 (2001), 1661-1674. (with E. El-Sedy) On happy numbers, Rocky Mountain Journal of Mathematics 30, Number 2, Summer 2000, 565-570. Descent on Picard groups using functions on curves, Bulletin of the Australian Mathematical Society 66 (2002), 119-124. (with A. Skorobogatov) On a Shimura curve that is a counterexample to the Hasse principle, to appear in Bull. London Math. Soc. On the diophantine equation x^2+2^k=y^n, to appear in Journal de Theorie des Nombres de Bordeaux. (with E. El-Sedy) On points of non-differentiability of convex functions, to appear in Journal of Applied and Computational Mathematics. (with J. Cremona) On the diophantine equation x^2+7=y^n, preprint. On the Brauer-Manin obstruction to the Hasse principle for curves of split Jacobians, preprint. Contact Details: Telephone: (00 968) 513 333 extn. 2407 Fax: (00 968) 515 490 Email: siksek@squ.edu.om or (better): samirsiksek@yahoo.com Postal Address: Department of Mathematics and Statistics College of Science P.O. Box 36 Sultan Qaboos University Al-Khod 123 Oman Back to staff list
Silverberg, Alice
University of California at Irvine. Arithmetic algebraic geometry, applications. Publications, slides, photographs, dances.
Alice Silverberg -- Home Page Alice Silverberg Professor of Mathematics and Computer Science University of California at Irvine Email is always the best way to reach me: asilverb@uci.edu Telephone: (949) 824-5422 Office: 219 MSTB Mailing Address: 103 MSTB Mathematics Department, UCI Irvine, CA 92697-3875 BIBLIOGRAPHY CURRICULUM VITAE MATH 120A, Fall 2005 MATH 234A, Fall 2005 OLD COURSE WEBSITES ***NEW!!!*** SOUTHERN CALIFORNIA SECURITY AND CRYPTOGRAPHY WORKSHOP , Saturday, September 24, 2005, University of California, Irvine. Center for Cyber-Security and Privacy, Bren School of Information and Computer Sciences, UC Irvine Slides from ANTS VI invited talk, June 15, 2004 (pdf file) PCMI Lecture Notes on Open Questions in Arithmetic Algebraic Geometry (525K PostScript file) MSRI Evans lecture, December 12, 2000 (unanimated slides) Emmy Noether in Erlangen Photos, Dances, and other Interesting Things
Shiu, Peter
Loughborough University. Elementary, analytic and computational number theory. Publications.
Peter's Homepage Peter Shiu's Homepage Department of Mathematical Sciences Loughborough University Loughborough Leicestershire LE11 3TU UK Telephone: +44(0)1509 223186 Fax: +44(0)1509 223969 email: P.Shiu@lboro.ac.uk Research Interests Elementary, analytic and computational number theory. Teaching Linear Algebra 1 : First Year Undergraduate Analysis : Second Year Undergraduate Number Theory : Final Year Undergraduate Professional Activities Reviewer of research papers in number theory for Zentralblatt fr Mathematik. London Mathematical Society representative on the Mathematical Sciences Committee of the British Associations for the Advancement of Science. Chairman of the United Kingdom Problem Group for the submission of problems for the International Mathematical Olympiad. Recent Publications Involutions associated with sums of two squares, Publications de L'Institute Mathematique, (73), (1996), 18-30. (MR 98c:11006, D. R. Heath-Brown; Zentralblatt 884.11008). Paul Erds (26 March 1913 - 20 September 1996), Mathl. Gaz. (1996), 602. Computations of the partition function, Mathl. Gaz., (1997), 45-52. (Zentralblatt 872.11041). Hua Loo-Keng, by Wang Yuan (Translated from Chinese by P. Shiu) Springer-Verlag (1998), ISBN 981-4021-03-2. Slower and longer when coming down!, Mathl. Gaz., (1999), 128-129. A function from Diophantine approximations, Publications de L'Institute Mathematique, (79), (1999), 52-62. More on Estermann and Pythagoras, Mathl. Gaz., (1999), 267-269. The distribution of totatives , with R. R. Hall. Submitted. A Diophantine property associated with prime-twins, Submitted. Other relevant information I am the father of the computer scientist Simon K. Y. Shiu and the number theorist Daniel K. L. Shiu. I am also the adopted-father of Amanda Waddingham and former foster-father of n - 3 persons, where 4 n 8. I enjoy playing poker, Go, bridge and chess (in this order of preference). [ Loughborough University | Academic Departments | Mathematical Sciences ] P.Shiu@lboro.ac.uk Last modified Sept 2000
Srinivasan , Anitha
IIT Bombay. Contact information.
Home Page of Anitha Srinivasan To the home page of Prof. Anitha Srinivasan Addresses : Office Address : Department of Mathematics, IIT Bombay , Mumbai, India 400 076 Home Address: SHA-9 IIT, Bombay 400076 Contact Information e-mail: anitha@math.iitb.ac.in Office Phone : 022 2576 7476 Home Phone : 022 2576 8476 Fax : 022 2572 3480 Research Area: Number Theory Personal Home Page
Savitt, David
McGill University and CICMA. Galois representations, modular forms, and p-adic Hodge theory. Publications, preprints, teaching and Canada USA Mathcamp.
David Savitt David Savitt Postdoctoral Fellow Department of Mathematics McGill University and CICMA 805 Sherbrooke St. W. Montreal, QC, H3A 2K6 Office: Burnside Hall 1129 Phone: (514) 398-3851 Fax: (514) 398-3899 E-mail: dsavitt(at)math(dot)mcgill(dot)ca My research is primarily in number theory, and specifically Galois representations, modular forms, and p-adic Hodge theory. I am also the Deputy Director of Canada USA Mathcamp, a summer program for high school students. In Winter 2005, I will teach Math 111: Mathematics for Education Students. Professional Information Mathcamp Personal Publications and Preprints University teaching Job application materials Math Links Canada USA Mathcamp home page Mathcamp teaching and related links AMS list of high school summer programs Photos Puzzles Frequently read websites To my chagrin, the most-read item that I have ever written is probably the Springer GTM Test .
Soundararajan, Kannan
University of Michigan. Analytic number theory.
UM Mathematics: Home People Graduate Program Undergraduate Program Research Courses General Information Computing Michigan Math Science Scholars Alumni Seminars Links Search Mathematics Search WWW Kannan Soundararajan Associate Professor PhD - Princeton University (734) 763-7867 ksound@umich.edu 2854 East Hall, Ann Arbor, MI 48109-1109 Areas of Expertise Number Theory Home Page My research involves the use of analytic methods in studying problems in number theory. My main interest is in the theory of L-functions; these are analytic objects which encode number theoretic data such as primes, class numbers of fields etc. A fundamental problem in the area is the Riemann hypothesis which predicts that the non-trivial zeros of L-functions all lie on a straight line. Two other significant questions concern the order of vanishing of L-functions at the central point, and the growth of L-functions inside the critical strip. My work is motivated by these questions: for example, Conrey and I recently exhibited the first infinite family of L-functions having no non-trivial real zeros. Some of my papers relating to these issues are 1. (with Conrey), Invent. Math. (150) pages 1-44 (2002). 2. Annals of Math. 152 (2000) 447-488. 3. (with Granville), The distribution of values of L(1,chi_d) Geometric and Functional Analysis, to appear. Preprint available on ArXiV Understanding the behaviour of L-functions can lead to the solution of simply stated number theoretic questions. For example Ono and I (Invent Math 130, 415-454) showed how the Riemann hypothesis for certain L-functions can be used to resolve a question of Ramanujan about which integers may be represented as x^2+y^2 +10z^2. In addition to L-functions I am also very interested in questions on primes and multiplicative functions; see my work with Montgomery (Beyond pair correlation, available on ArXiV) and my work with Granville (Ann. of Math., 153, 407-470). I am also interested in attractive problems in elementary combinatorial number theory, although I have not worked in this area recently. Department of Mathematics | 2074 East Hall | Ann Arbor, MI 48109-1109 Phone: 734.764-0335 | Fax: 734.763-0937 The page last modified Thursday, 12-Feb-2004 15:36:43 EST Site errors should be directed to math-webmaster@umich.edu College of Literature, Science Arts University of Michigan Regents of the University of Michigan , Ann Arbor, MI 48109 USA
Sharifi, Romyar
McMaster University. Algebraic Number Theory and Arithmetic Algebraic Geometry. Publications, slides, thesis.
Romyar's web page Romyar Sharifi Assistant Professor of Mathematics Canada Research Chair Dept. of Mathematics and Statistics McMaster University 1280 Main Street West Hamilton, Ontario L8S 4K1 Canada Office: Hamilton Hall 412 Phone: (905) 525-9140 Fax: (905) 525-2143 Email: sharifi "at" mcmaster.ca Research Interests Algebraic Number Theory and Arithmetic Algebraic Geometry Curriculum Vitae HTML or PDF Teaching Math 705, Algebraic Number Theory Publications Iwasawa theory and the Eisenstein ideal submitted for publication (version 3 20 2005) Massey products and ideal class groups submitted for publication (version 10 15 2005) On the failure of pseudo-nullity of Iwasawa modules with Y. Hachimori, Journal of Algebraic Geometry (2005) (journal version) A cup product in the Galois cohomology of number fields with W. McCallum, Duke Mathematical Journal (2003) (journal version, related computations) Relationships between conjectures on the structure of pro-p Galois groups unramified outside p Arithmetic Fundamental Groups and Noncommutative Algebra, Proceedings of Symposia in Pure Mathematics (2002) Determination of conductors from Galois module structure Mathematische Zeitschrift (2002) (journal version) Minimal conductors of Kummer extensions by roots of unit elements Journal of the Ramanujan Mathematical Society (2001) On norm residue symbols and conductors Journal of Number Theory (2001) (journal version) Ramification groups of nonabelian Kummer extensions Journal of Number Theory (1997) (journal version) On cyclotomic polynomials, power residues and reciprocity laws L'Enseignement Mathmatique (1997) Thesis Twisted Heisenberg representations and local conductors The University of Chicago (1999) Misc. Writings Notes and slides from talks, etc...
Sinisalo, Matti K.
GeraCap Ltd. Algorithms in number theory, Computer algebra. Publications.
Matti K. Sinisalo's homepage Matti K. Sinisalo's homepage Name: Matti K. Sinisalo Education: Ph. Lic. in mathematics, University of Oulu , 1994. Born: 1961 in Muonio My CV Special Interests: Algorithms in Number Theory, Computer Algebra , Elementary and Algebraic Number Theory, Error Correcting Codes, Cryptology, Digital Signal Processing, Finite Fields, Elliptic Curves Publications: Matti K. Sinisalo: On the minimal cycle lengths of the Collatz sequences, Preprint, June 2003, University of Oulu ( WORD ). Matti K. Sinisalo: Fareyn luvut ja Mathematica (Farey sequences and Mathematica, in finnish), in Logic, mathematics and computer, Publications of Finnish Society of Artificial Intelligence, symposium serie, No 14, 1996, pp. 243-249 ( PDF ). Matti K. Sinisalo: Carmichaelin lukujen konstruktioista, Esitelm lukuteorian pivill 1995 (in finnish) ( PDF ). Matti K. Sinisalo: Checking the Goldbach conjecture up to 4*10^11, Mathematics of Computation, 61 (204), pp. 931-934, October 1993. Matti K. Sinisalo: Solutions of the Congruence 2^(n-2) = 1 (mod n) up to 10^ 11, Preprint, Department of Mathematics, University of Oulu, 1991 ( PDF ). Hobbies: -International Radio Amateur Certificate in Technical Class:CEPT B, Harmonized Amateur Radio Examination Certificate, HAREC, CEPT Recommendation T R 61-02. -Youth soccer training in RoPS . Links: A-2 vapaat sanat nelikirjaimisessa aakkostossa (in Finnish) Bibliography of Computer Algebra Javala (Java-oppimisymprist, in Finnish) Leikki alkuluvuilla (in Finnish) MathForum, MathWorld Miljoonan dollarin palkkio ... (in Finnish) Nokia Number Theory Web RSA-esitelm (in Finnish) RSA Challenge Numbers SMFL Symbian Tapahtumat (in Finnish) University of Oulu Zentralblatt - database of mathematics Email: matti.sinisalo at pp5.inet.fi geovisit();
Stoll, Michael
International University Bremen. Arithmetic Geometry; Combinatorics; Mathematical Biology; Group Theory; Galois Theory. Publications, notes, MAGMA code, tables of genus-2 curves.
Michael Stoll's Homepage Dr. Michael Stoll, Prof. of Mathematics International University Bremen School of Engineering and Science P.O.Box 75 05 61 28 725 Bremen, Germany m.stoll@iu-bremen.de IUB Directory Entry This picture was taken by William Stein in Oberwolfach in July 2005. Mathematics Colloquium at IUB Papers and preprints Oberseminar Gttingen-Hannover-IUB: Next meeting Nov 25 in Hannover Talk notes Workshop "Rational Points on Curves - Explicit Methods", July 2005 at IUB Teaching at IUB Introductory Algebra, Fall 2005 Introductory Geometry, Fall 2005 Perspectives of Mathematics, Fall 2005 Past Teaching Files from Magma Workshop at IHP Programs (e.g. ratpoints) Genus 2 curves with small odd discriminant Michael Stoll, Tue Nov 1, 2005
Shallit, Jeffrey O.
University of Waterloo. Algorithmic number theory (primality testing, and factoring), formal languages and automata theory (especially connections with number theory), history of mathematics and computer science, ethical use of computers.
Home page of Jeffrey O. Shallit Jeffrey O. Shallit Professor School of Computer Science University of Waterloo Waterloo , Ontario N2L 3G1 Canada Office: Davis Centre 3134 Telephone: (519) 888-4804 Fax: (519) 885-1208 E-mail: GPS: 43 28' 21" N; 80 32' 32" W If you send me e-mail and don't get a response, it may be that I have blacklisted your domain. I am not currently accepting mail from the following domains: azlyrics.com, puremail.com, flashmail.com, puremail.net, support.com, technet.ms.com, bulletin.com, freemail.com, rocketmail.com, noone.com, updates.com, playsite.de, web.de, notmydesk.com, luftmensch.com, support.net. Areas of interest: Combinatorics on words, formal languages and automata theory (especially connections with number theory), algorithmic number theory (primality testing, factoring, etc.), history of mathematics and computer science, ethical use of computers, debunking pseudoscience and pseudomathematics. See my rating at ratemyprofessors.com. Professional Activities Automatic Sequences: Theory, Applications, Generalizations , Cambridge University Press, July 2003. Algorithmic Number Theory published by MIT Press, August 1996. Editor-in-chief, Journal of Integer Sequences Center for Applied Cryptographic Research Courses taught by JOS Curriculum vitae of JOS Selected papers of JOS Recent talks by JOS Book reviews by JOS Published and unpublished essays by JOS Graduate students supervised by JOS Library catalogues Links to other CS and math-related sites This week's Math CS talks at Waterloo Vice-President, Electronic Frontier Canada Unprofessional Activities Family Friends Quotations Letters to the editor by JOS Community Editorial Board JOS's favorite animal (Also visit here .) My Elvis number Travel Photographs Other interesting web pages Urban Legends Debunked Today's weather in Kitchener-Waterloo Disclaimer: Nothing on this page should be taken to represent the official views of the University of Waterloo.
Schoof, Rene
Universit di Roma Tor Vergata. Algebraic number theory, arithmetic geometry. Papers, preprints, lecture notes, resources, tables.
Ren Schoof, Universit di Roma TOR VERGATA, Rene Schoof Ren Schoof Address Universit di Roma Tor Vergata Dipartimento di Matematica Via della Ricerca Scientifica I-00133 Roma, ITALY Phone: +39-06-72594662 Fax: +39-06-72594699 Email: schoof@mat.uniroma2.it schoof@science.uva.nl Anno accademico 2005-2006 Corso di Geometria ed Algebra (Colleferro) Corso di Teoria elementare dei numeri (Ingegneria Informatica) Anni precedenti 2000-2005 Publications Papers and Preprints Other Agrawal-Kayal-Saxena primality test Tables of curves over finite fields with many points Zeroes of the Riemann zeta function Largest prime number. This week's seminars in Rome Node in the M.I.U.R. cofin 2004 project GVA Various Take a walk in the Jordaan from here Maartens
Sofer, Adriana
University of Texas at Austin. Contact and teaching information.
Home Page of Adriana Sofer Adriana Sofer office: RLM 11.166, phone: 512-471-1135, fax: 512-471-9038 mailing address: Department of Mathematics, 1 University Station C1200, Austin, TX 78712-0257 asofer@math.utexas.edu Teaching Spring 2003: M328K Fall 2003: M341 Spring 2004: M328K Fall 2004: M341 Spring 2005: M326K Fall 2005: M325K Outreach Visit the Elementary School Math Club , a lesson plan for educators in UTOPIA UT Math home page UT home page UT Direct Send questions, comments to: asofer@math.utexas.edu
Smyth, Chris
Edinburgh University. Algebraic number theory, especially algebraic integers which are constrained in some way; algorithmic aspects of algebraic curves; combinatorial aspects of network design. Recent publications.
Chris Smyth Chris Smyth's minimalist home page. Misc Hamilton's Bridge over the Royal Canal, Dublin Misc JA2007 Misc James Cook Mathematical Notes Clark's Nutcracker Four herons in Regent's Park, London, 25 March 2005 (photo: Dan Salter) Family photos: you have been warned! AKS Recent preprints and papers N. Berry, A. Dubickas, N.Elkies, B. Poonen and C J Smyth, The conjugate dimension of algebraic numbers . Click here for .ps file or here for xxx archive C J Smyth, Explicit formulas for the Mahler measure of families of multivariable polynomials. Click here for .ps file. J McKee and C J Smyth, There are Salem numbers of every trace. Click here for .ps file or here for xxx archive J McKee and C J Smyth, Salem numbers of trace -2 and traces of totally positive algebraic integers. Click here for .ps file 2003: A Dubickas and C J Smyth, On metric heights , Periodica Math. Hung. 46 (2)(2003), 135-155. 2002: F Beukers and C J Smyth, Cyclotomic points on curves. In: Number Theory for the Millenium I, A.K. Peters 2002 ( Proceedings of the Millennial Conference on number theory, Urbana May 21-26 2000), 67-85. Click here for .ps file. C J Smyth, An explicit formula for the Mahler measure of a family of 3-variable polynomials. J. Theor. Nombres Bordeaux 14 (2002), 683-700.Click here for .ps file. A Dubickas and C J Smyth, Variations on the theme of Hilbert's Theorem 90. Glasgow Math. J. 22 (2002), 435-441. Click here for .ps file. -- Edinburgh University School of Maths home page Chris Smyth (chris@maths.ed.ac.uk)
Somodi, Marius
University of Northern Iowa. Witt equivalence of algebraic number fields.
Marius Somodi - Department of Mathematics - UNI Favorite links: Census bureau A book search engine American Mathematical Society Marius Somodi Assistant Professor of Mathematics Department of Mathematics Wright 316 University of Northern Iowa Cedar Falls, IA 50614 Tel: 319-273-6263 E-mail: somodi @ uni.edu Teaching (Fall 2005) Introduction to Statistical Methods (800-072 Sections 5 and 6) Schedule (Fall 2005) Monday Tuesday Wednesday Thursday Friday 9-10 Office hour Office hour Office hour 10-11 072 072 072 11-12 072 072 072 12-1 Office hour 1-2
Swinnerton-Dyer, Sir Peter
University of Cambridge. FRS. Lecture notes.
Prof. Sir Peter Swinnerton-Dyer, FRS Department of Pure Mathematics and Mathematical Statistics DPMMS People Prof. Sir Peter Swinnerton-Dyer, FRS Prof. Sir Peter Swinnerton-Dyer, FRS Title:Emeritus Professor Email: H.P.F.Swinnerton-Dyer@dpmms.cam.ac.uk College:Trinity College College:St Catharine's College Room: E1.10 Tel: +44 1223 766851 Personal Home Page Research Interests: Number Theory 2003-2005 Department of Pure Mathematics and Mathematical Statistics, University of Cambridge Information provided by webmaster@dpmms.cam.ac.uk
Scholl, Anthony J.
University of Cambridge. Number theory, arithmetic algebraic geometry, modular forms. Preprints, notes.
Prof. A.J. Scholl Department of Pure Mathematics and Mathematical Statistics DPMMS People Prof. A.J. Scholl Prof. A.J. Scholl Title:Kuwait Professor of Number Theory and Algebra Email: A.J.Scholl@dpmms.cam.ac.uk Room: E1.05 Tel: +44 1223 765889 Personal Home Page Research Interests: Number theory, arithmetic algebraic geometry, modular forms 2003-2005 Department of Pure Mathematics and Mathematical Statistics, University of Cambridge Information provided by webmaster@dpmms.cam.ac.uk
Sun, Zhi-Wei
Nanjing University. Number theory (especially combinatorial number theory); Combinatorics; Group theory; Mathematical logic. Papers and lectures.
Zhi-Wei Sun's Home Page Initial day: July 31, 2001 Last modified: 2005-11-01 visits since April 10, 2002 Zhi-Wei Sun Department of Mathematics Nanjing University Nanjing 210093 People's Republic of China E-mail: zwsun@nju.edu.cn Telephone: +86-25-83594840 Office in the Dept.: Room 103 Last Name Sun First Name Zhi Wei Date of Birth October 16, 1965 Place of Birth Lianshui County, Jiangsu Province, China Research Interests Number Theory (especially Combinatorial Number Theory), Combinatorics, Group Theory, Mathematical Logic. Academic Service Reviewer for Mathematical Reviews, 1992--. Member of the American Mathematical Society, 1993--. Referee for J. Number Theory, European J. Combin., Discrete Math., Fibonacci Quart., SIAM Review, Publ. Math. Debrecen, Aequationes Math., Math. Slovaca, INTEGERS etc. School Education and Employment History 1980.9--1983.7 The High Middle School Attached to Nanjing Normal Univ. 1983.9--1992.6 Department of Mathematics, Nanjing University (Undergraduate--Ph. D. Candidate; B. Sc. 1987, Ph. D. 1992) 1992.7-- Teacher in Department of Mathematics, Nanjing University 1994.4--1998.3 Associate Professor in Math. 1998.4-- Full Professor in Math. 1999.11- Supervisor of Ph. D. students Research Grants Awards and Honours Academic Visits Courses Taught and Ph.D Students List of Publications ( by Field ) Books and Papers Citing Sun's Work Notes on Conjectures of Z. W. Sun Introduction to Sun's Papers on Covers The Webpage of Wall-Sun-Sun Prime Covers, Sumsets and Zero-sums (by Sun) Invited Lectures in Mathematics 01. Simple Ideas for Famous Problems , 1996. 02. Various Number-theoretic Quotients and Related Congruences , 2000. 03. Recent Progress on Covers of the Integers and Their Applications , 2000. 04. On Hilbert's Tenth Problem and Related Topics , 2000. 05. Recent Progress on Combinatorial Number Theory (Chinese), 2001. 06. Equalities and Inequalities Related to Covers of Z or Groups , 2002. 07. On the Structure of Periodic Arithmetical Maps , 2002. 08. New Results on Subset Sums , 2002. 09. On Zero-sum Problems , 2002. 10. On the Sum $\sum_{k\equiv r (mod m)}\binom nk$ and Related Results , 2002. 11. Introduction to Bernoulli and Euler Polynomials , 2002. 12. Problems and Results in Combinatorial Number Theory , 2002. 13. Sumsets with Polynomial Restrictions , 2002. 14. The Magic of Mathematics (Chinese), 2002. 15. How to Unify Covering Systems, Restricted Sumsets and Zero-sum Problems , 2003. 16. Recent Progress on Zero-sum Problems and Snevily's Conjecture , 2004. 17. Covering Systems and their Connections to Zero-sums , 2004. 18. On Disjoint Systems of Residue Classes or Cosets of Subgroups , 2004. 19. On Various Combinatorial Sums and Related Identities , 2004. 20. Two Local-Global Theorems and a Powerful Formula , 2004. 21. Groups and Combinatorial Number Theory , 2004. 22. On Some Conjectures of Erdos-Heilbronn, Lev and Snevily , 2004, 2005. 23. Identities and Congruences for Bernoulli and Euler Polynomials , 2005. 24. Problems and Results on Covering Systems , 2005. 25. Some Congruences Motivated by Algebraic Topology , 2005. Selected Photoes 01. at Venice (Venezia) , Florence (Firenze) , Genova , Rome (Roma) 02. at Trieste , Vienna (Wien) , Graz , Lyon , Bordeaux , Pacific , Irvine 03. with Prof. M. Agrawal (famous for the AKS primality test) at ICTP, Trieste (2004) 04. with Prof. R. Schoof (famous for Schoof's algorithm) at Rome (2004) 05. with Prof. A. Perelli at Genova (2004) 06. with Prof. A. Geroldinger and his wife at Graz (2004) 07. with Prof. R. Sprugnoli, D. Merlini and D. G. Rogers at Florence (2004) 08. with Prof. R. P. Stanley at Tianjin (2004) 09. with Prof. R. A. Askey and J. Zeng at Tianjin (2004) 10. with Prof. Y. Bilu at Bordeaux (2005) 11. with Prof. J. Zeng and Prof. J. L. Nicolas at Institute of Camille Jordan (2005) 12. Photoes on the Integers Conference 2005 (West Georgia Univ., Oct. 27-30): Prof. R. L. Graham , the Graham couple , Prof. C. Pomerance , Prof. M. B. Nathanson , Prof. Fan Chung and M. B. Nathanson , Prof. B. Landman ; with Prof. R.L. Graham and Fan Chung , C. Pomerance and S. Wagstaff , D. Zeilberger , with Prof. M. B. Nathanson , H. Diamond and D. Goldston , B. Landman , S. Milne , with Prof. A. Bialostocki , T. Brown , K. O'Bryant and R. L. Jin , V. F. Lev . Curriculum Vitae of Zhi-Wei Sun ( Word file ) Zhi-Wei Sun has the copyright of those unpublished materials at this website. The copyright of each published or accepted paper is held by the corresponding publisher.
Siligardos, Giorgos
University of Crete. Number theory; technical analysis.
Giorgos Siligardos Mathematician, Ph.D. E-mail: siligard@tem.uoc.gr Homepage http: www.tem.uoc.gr ~siligard Teaching Lectures Ph. D. Master Publications On Pure Mathematics Publications On Technical Analysis To Appear Submited for Publication Working Papers Daedalus Teaching Winter 2005 Courses: Introduction to Derivatives (Technological Institute of Crete) Portfolio Management and Investment Analysis (Technological Institute of Crete) TOP Lectures Old Lectures Series of Lectures in Technical Analysis ( University of Crete ) Option Derivatives. Trading Hedging (28, 29 July 2004, Summer School in Math. Department , University of Crete ) Volume Interpretation in Chart Analysis (23 March 2005, Department of Economics , University of Crete ) TOP Representation of powers of primes via binary quadratic forms ( ) TOP Primes of the form x+ny ( x+ny) TOP Publications on Pure Mathematics The Embedding Problem and Representation of Prime Powers by Quadratic Forms Journal of Number Theory 85, 305-319(2000) On Power Residue Quadratic Characters of Units and the Representation of Numbers by Quadratic Forms ACTA ARITHMETICA V99,67-77(2001) Numerical Approach to an Embedding Problem Concerning Dihedral Class Fields of Order 16 Bulletin of The Greek Mathematical Society V48, 2003 (77-84) Proccedings, 4th Panhellenic Conference on Algebra Number Theory,Univ. of Patras, 2002 TOP Publications on Technical Analysis The Concept of Equivalence Technical Analysis of Stocks and Commodities,V.21:2,(60-63),February 2003 Reverse Engineering RSI II Technical Analysis of Stocks and Commodities,V.21:6,(18-30),June 2003 Reverse Engineering RSI II Technical Analysis of Stocks and Commodities, V.21:8,(36-43),August 2003 Mechanically Recognizing Triangular Formations Technical Analysis of Stocks and Commodities, V.22:3,(24-38), March 2004 The Decomposition Method Technical Analysis of Stocks and Commodities, V 22.9, September 2004 Spike Up The Volume Technical Analysis of Stocks and Commodities, V 23.6, June 2005 TOP To appear Handling The Cup Technical Analysis of Stocks and Commodities TOP Daedalus Daedalus is an add-on for Metastock created by Giorgos Siligardos. Information about its features and capabilities can be found in the Daedalus User's Guide page. Metastock is a registered trademark of Equis International. TOP Free counter
Shlapentokh, Alexandra
East Carolina University. Diophantine decidability. Publications.
Alexandra Shlapentokh Alexandra Shlapentokh Professor Department of Mathematics East Carolina University Greenville, NC 27858-4353 Office: Austin 231 Phone: 252-328-4108 Fax: 252-328-0911 mailto:shlapentokha@ecu.edu Teaching Research
Shonhiwa, Temba
University of Zimbabwe. Number theory, combinatorics, algebra.
Temba Shonhiwa Dr Temba Shonhiwa Chairman Room Number: 226, New Wing Extension: 1177 Email: temba@maths.uz.ac.zw Specialty: Number Theory, Combinatorics Courses taught: MTH005 Algebra 1 MTH007 Number Theory Personal details
Song, Joungmin
Rice University. Analytic number theory: mean value theorems for multiplicative functions, sieve methods and circle methods.
Joungmin Song
Scheidler, Renate
University of Calgary. Algorithms for computing invariants of number fields and function fields.
Renate Scheidler Renate Scheidler Associate Professor, Department of Mathematics Statistics Associate Professor, Department of Computer Science Research Associate, Alberta Informatics Circle of Research Excellence (iCORE) Address: Room 364, Mathematical Sciences Building Department of Mathematics Statistics University of Calgary 2500 University Drive NW Calgary , Alberta, Canada T2N 1N4 Telephone: (403) 220-6628 Fax: (403) 282-5150 E-mail: rscheidl@math.ucalgary.ca rscheidl@cpsc.ucalgary.ca rscheidl@ucalgary.ca Web Site: http: www.math.ucalgary.ca ~rscheidl My research interests include number theory and cryptography. More specifically, my work focuses on the development and implementation of algorithms for computing invariants of number fields and function fields as well as exploring these fields for cryptographic applications. Research Interests: Algorithmic Number Theory Number Theoretic Cryptology Courses: Fall 2005: PMAT 529 603.45 Modern Cryptography and Cryptanalysis Winter 2006: CPSC 313 Introduction To Computability Office Hours: by appointment (send me e-mail ) Publications Biographical Information Research Links CISaC (Centre for Information Security and Cryptography) IQIS (Institute for Quantum Information Science) ATIPS (Advanced Technology Information Processing Systems) CLIAS (Calgary Laboratory for Information Assurance and Security) Last modified by Renate Scheidler
Schmitt, Susanne
Max-Planck-Institut fr Informatik. Effective computational geometry, separation bounds; Computer algebra; Algebraic number theory, elliptic curves. Publications.
Homepage: Susanne Schmitt (Max-Planck-Institut fr Informatik) Department 1: Algorithms and Complexity max planck institut informatik Homepage Susanne Schmitt Max-Planck-Institut fr Informatik Department 1: Algorithms and Complexity Building 46.1 , Room 318 Stuhlsatzenhausweg 85 66123 Saarbrcken Germany Email: Get my email address via email Phone: +49 681 9325 118 Fax: +49 681 9325 199 Research Interests Real algebraic numbers, Root isolation, Separation bounds Effective Computational Geometry Computer Algebra Algebraic number theory, Elliptic curves Publications Publications of Dr. Susanne Schmitt Teaching Summer term 2005: Seminar Geometrische Algorithmen, Dr. Susanne Schmitt, Dr. Nicola Wolpert Earlier terms Winter term 2004 2005: Seminar Geometric Rounding, Dr. Lutz Kettner, Dr. Susanne Schmitt Winter term 2004 2005: Lecture Exakte und Effiziente Algorithmen fr Kurven und Flchen, Dr. Lutz Kettner, Dr. Susanne Schmitt, Dr. Nicola Wolpert Summer term 2004: Seminar Theorie und Praxis geometrischer Algorithmen, Dr. Susanne Schmitt, Dr. Nicola Wolpert Winter term 2003 2004: Lecture Effective Computational Geometry for Curves and Surfaces, Dr. Lutz Kettner, Dr. Susanne Schmitt, Dr. Nicola Wolpert Summer term 2001: Lecture Einfhrung in Algorithmen und Datenstrukturen, Dr. Susanne Schmitt, Dr. Elmar Scher Summer term 2000: Algorithmische Zahlentheorie, Dr. Susanne Schmitt, Prof. Dr. Horst G. Zimmer Summer term 1999: Elliptische Kurven, Dr. Susanne Schmitt CV Education April 1999: Ph. D. in Mathematics at the Universitt des Saarlandes, Saarbrcken Title of thesis: Bestimmung der Mordell-Weil Gruppe elliptischer Kurven ber algebraischen Zahlkrpern (supervisor: Prof. Dr. H. G. Zimmer ). October 1991 - June 1995: Studies in Mathematics at the Universitt des Saarlandes, Saarbrcken Title of Diploma Thesis: Berechnung der Mordell-Weil Gruppe parametrisierter elliptischer Kurven (supervisor: Prof. Dr. H. G. Zimmer ). Recent positions October 2000 - present: Research assistant in Max-Planck-Institut fr Informatik June 1995 - October 2000: Research assistant in Mathematics at the Universitt des Saarlandes, Saarbrcken Projects EXT : LEDA real extended Real Root isolation: Descartes method for polynomials with interval coefficients, Descartes method for polynomials in Bernstein basis (with interval coefficients) Copyright 2005 by Max-Planck-InstitutInformatik | Impressum page last modified Wednesday, 01 June 2005 - 13:48 Susanne Schmitt: R esearch Interests P ublications T eaching C V P rojects Search MPII (type ? for help)
Snaith, Nina
University of Bristol. Random matrix theory and zeta and L-functions. Offers publications and research projects.
Nina Snaith's Home Page Nina Snaith Home Publications Mathematics Home Nina Snaith School of Mathematics, University of Bristol, University Walk, Clifton, Bristol. BS8 1TW Telephone: +44 (0)117 928-9838 Fax: +44 (0)117 928 7999 Email: n.c.snaith (add @bristol.ac.uk) Position: Lecturer Research interests: While belonging to the quantum chaos group at Bristol, my particular interest at the moment is the connection between Random Matrix Theory and certain number theoretical functions such as the Riemann zeta function and L-functions. This connection arises through the statistics of the zeros of these functions and can be exploited, allowing us to study zeta and L-functions using the techniques of Random Matrix Theory. Errata to the proceedings volume Recent Perspectives in Random Matrix Theory and Number Theory, edited by Francesco Mezzadri and Nina Snaith Word pdf
Rubin, Karl
University of California, Irvine. Arithmetic algebraic geometry. Publications, lecture notes.
Karl Rubin
Ramakrishnan, B.
Harish-Chandra Research Institute. Number theory and automorphic forms.
B.Ramakrishnan HRI AboutHRI Mathematics Physics Visitors Opportunities Address Search Mathematics: Research People Graduatestudies Activities Timetable B.Ramakrishnan Email address ramki at mri dot ernet dot in Areas of interest Number theory, and automorphic forms Home page Read more about B.Ramakrishnan . Mathematics: Research People Graduatestudies Activities Timetable HRI AboutHRI Mathematics Physics Visitors Opportunities Address Search Harish-Chandra Research Institute Chhatnag Road , Jhusi Allahabad 211019 , India Phone: +91(532)2667510, 2667511, 2668311, 2668313, 2668314 Fax: +91(532)2567748, 2567444 About this page ; HRI Webadmin webadmin at mri dot ernet dot in Updated: 2004-11-08T10:43:35Z
Rouse, Jeremy
University of Wisconsin-Madison. Number theory, with particular interest in elliptic curves and modular forms; Combinatorics. Publications.
Jeremy Rouse
Robertson, Leanne
Smith College. Algebraic number theory; Class groups and class numbers; Power integral bases; Cyclotomic fields. Publications.
Leanne Robertson's homepage Leanne Robertson Assistant Professor Department of Mathematics Smith College Northampton, MA 01063 Office: 311 Burton Hall voice: 413-585-3861 fax: 413-585-3786 email: lroberts@math.smith.edu Office Hours: Monday 2-3 Tuesday 9-10 Thursday 1:30-2:30 and by appointment Courses: MTH 105 Discovering Mathematics MTH 111 Calculus MTH 153 Discrete Mathematics MTH 211 Linear Algebra (Fall 2005) MTH 224 Geometry MTH 233 Modern Algebra MTH 238 Number Theory MTH 307 Topics in Math Education MTH 333 Topics in Abstract Algebra (Topic Spring 2004: Algebraic Number Theory) Education: Ph. D. University of California at Berkeley B.A. Reed College Research Interests: Algebraic number theory Class groups and class numbers Power integral bases Cyclotomic fields Publications (pdf file with abstracts) I am a member of the Five College Number Theory Seminar . Useful links for students: A Guide to Mathematics at Smith College Summer Research Opportunities for Students Budapest Semester in Mathematics Hudson River Undergraduate Math Conference Biographies of Women in Mathematics Careers involving Mathematics || Smith College Mathematics Department || Smith College ||
Rubinstein, Michael
University of Waterloo. Experimental number theory. Publications, software for L-functions, tables of modular polynomials.
Michael Rubinstein Can be reached at: mrubinst at uwaterloo dot ca Pure Maths, U of W 200 University Ave W Waterloo, Ontario, N2L 3G1 Canada Math: Workshop on Number Theory and Random Matrix Theory Curriculum Vitae: pdf L C++ class library and command line program for computing zeros and values of L-functions. Includes data. Publications Modular Polynomials class: math 135 Music: The Conspiracy of Equal Temperament. An essay on tunings. Why 12 notes to the octave? Includes a proposal for a 19 note octave (not meant to replace the 12 note octave). I finally gave in and put some of my old music on the web. Only for the seriously bored. Misc: The Early Years (1971-74) Warning! The end of the world as we know it is 40000 years overdue! Read about it here. How to tell if your head is gonna explode. Take the HCE test. Some of my sketches . I no longer sketch. Look out for strangelets ! The post humanity era is approaching fast! 2030 at the latest. Sell your stocks while you can. Head's up . Feb 1, 2019. Book your plane ticket to a safe spot now. Lawn Chair Larry . Don't try this at home. Scrotum self repair . Don't try this either. Ouch. Stop space billboards now and enjoy the night sky of the remaining pre post humanity years. Stay current . Are they dangerous ? Don't abuse goats . Snowball's revenge. Posing with the L-function calculator. This man has too much money. Number of times this page has been accessed:
Raghuram, A.
Tata Institute of Fundamental Research. Langlands Program: Representation theory of p-adic groups; Automorphic representations and their associated L-functions. Papers and thesis.
Raghuram's homepage Raghuram's Homepage Quick Links: Address Contact Information Teaching Research Interests Publications Preprints Notes Service Cool Stuff Address for Correspondence: Department of Mathematics University of Iowa 14 MacLean Hall Iowa City, IA 52242-1419, USA. e-mail : araghura@math.uiowa.edu (araghura {at} math {dot} uiowa {dot} edu) Click here for my official webpage by the Department of Mathematics of UI. Click here for my CV. Contact Information: Office: 325F, MacLean Hall. Phone: (319)-335-3863. Office Hours: By appointment. Back to the top. Teaching: Click here for my teaching statement. Click here for some excerpts from teaching evaluations. Fall 2003: 22M150 (Discrete Mathematics), 22M027 (Linear Algebra). Spring 2004: 22M026 (Calculus-II) Fall 2004: 22M150 (Discrete Mathematics), 22M026 (Calculus-II). Spring 2005: 22M330 (Topics in Algebra: Introduction to Representation Theory.) Fall 2005: 22M126 Elementary theory of numbers. Fall 2005: 22M330 Topics in Algebra: Introduction to Linear Algebraic Groups. Back to the top. Research Interests: Click here for my research statement. My research interests are broadly in the Langlands Program. More specifically I work in the interface of Representation theory of p-adic groups, Automorphic representations and their associated L-functions. Back to the top. Publications in Refereed Journals and Conference Proceedings: 1. (With D. Prasad) Kirillov theory for GL_2(D) where D is a division algebra over a non-Archimedean local field, Duke Math. Journal, Vol. 104, No. 1, 19--44 (2000). [pdf] 2. (With M. Ram Murty) Some variations on the Dedekind conjecture, Journal of the Ramanujan Math. Society, 15, No. 2, 75--95 (2000). [dvi] 3. On representations of p-adic GL_2(D) Pacific Journal of Mathematics. 206, No. 2, 451--464, (2002). [dvi] 4. Nonvanishing of certain Rankin-Selberg Convolutions, C. R. Math. Acad. Sci. Soc. R. Can. 24, No. 2, 67--71 (2002). [dvi] 5. (With Joshua Lansky) A remark on the correspondence of representations between GL(n) and division algebras. Proceedings of the Amer. Math. Soc., 131, No. 5, 1641--1648, (2003). [dvi] 6. (With Joshua Lansky) On conductors and newforms for U(1,1). Proceedings of the Indian Academy of Sciences. 114, No. 4, 319--343, (2004). 7. Kirillov theory for GL_2(D), Proceedings of the Conference on L-functions and Cohomology of Arithmetic groups, TIFR, Mumbai, December 1998. Somehow I do not have an electronic version of this paper, but I have lots of reprints! 8. Nonvanishing of L-functions of cusp forms inside the critical strip. Proc. Int. Conf.-Number Theory , Lecture Note Series, Ramanujan Math. Soc., No. 1, 97-105, (2004), [dvi] 9. On the restriction to D* x D* of representations of p-adic GL_2(D). 19 pages, (2005). To appear in the Canadian Journal of Mathematics . [dvi] 10. A Kunneth theorem for p-adic groups. 7 pages, (2005). To appear in the Canadian Mathematical Bulletin. [dvi] Click here to see my publications as it shows up on MathSciNet. Click here for a list of my publications with abstracts. Back to the top. Preprints: 1. (With Joshua Lansky) On conductors and newforms for SL(2). 27 pages, (2003). Submitted. [dvi] 2. Quadratic reciprocity for root numbers of GL(2). 13 pages, (2004). Submitted. [dvi] 3. (With Freydoon Shahidi) On the special values of symmetric power L-functions of cusp forms on GL(2). In preparation. Back to the top. Notes, Surveys, Thesis: 1. Ph.D. thesis. The thesis is about 100 pages. This thesis studies some aspects of the representation theory of GL(2,D) for a p-adic division algebra D. 2. (Ram Murty) Lectures on Artin L-functions. These are the expanded version of the notes of a course Ram Murty gave in Dec '98 - Jan '99 in TIFR during the special year on Automrphic forms. (41 pages) [dvi] These notes have appeared as an expository paper by Ram Murty in JRMS. The specific reference is: Journal of the Ramanujan Math. Soc., 16, No. 3, 261--307, (2001). 3. (With Dipendra Prasad) Representation theory of GL(n) over non-Archimedean local fields. These are the notes of a course given by Dipendra Prasad in the workshop "Automorphic forms on GL(n)" held at ICTP, Trieste, Italy in August 2000. (41 pages) [dvi] 4. (With B. Sury) Groups acting on trees. These are the notes of a course that Sury and I gave at the instructional school on Geometric Group Theory at IIT--Guwahati, in December 2002. Send me an email if you want to see these notes. 5. Introduction to representation theory. In preparation. These are the notes of a course I taught at the University of Iowa in Spring 2005. Back to the top. Service: 1. Regular contributor to Math Reviews. Click here to see the reviews I have written. (Including a featured review of the 2002 Annals of Math paper of Kim and Shahidi.) 2. Co-organizer with N.S.N. Sastry of a three week workshop on Algebraic Groups in December 2006 at Indian Statistical Institute, Bangalore, India. Keep an eye out for more announcements about this workshop. 3. Member of the library committee at the University of Iowa. 4. Referee work for Journal of the Ramanujan Mathematical Society and Proceedings of the Indian Academy of Sciences. Back to the top. Cool Stuff: American Mathematical Society Number Theory Web This site has links to the homepages of more than a thousand number theorists. To quote Godement (Chapter 3 of his notes on Jacquet-Langlands) "Salvation through zahlentheorie..." Pink Floyd The greatest rock band...... Last Modified on September 15, 2005.
Rose, Harvey
University of Bristol. Problems concerning small classes of recursive functions; Number theory of elliptic curves. Publications, teaching material.
Harvey Rose's Home Page Harvey Rose's Home Page Lecturer in Pure Mathematics Office: 2.3 St.Michael's House Tel. (0117)3311666 E-mail: H.E.Rose@bristol.ac.uk School of Mathematics, University of Bristol, Clifton, Bristol, BS8 1TW, UK Research interests Problems concerning small classes of recursive functions. Number theory of elliptic curves. Group theory Recent publications "Linear Algebra, A Pure Mathematical Approach" (2002). 264 pages, Birkhauser, Basel Teaching Group theory 3
Rohrlich, David
Boston University. Number theory. Preprints, errata.
David Rohrlich's Home Page David Rohrlich's Home Page Contact Information Department of Mathematics and Statistics Boston University Boston, MA 02215 (617) 353-9545 rohrlich@math.bu.edu. Erratum A deformation of the Tate module, J. of Algebra 229 (2000), 280 -- 313. The error occurs in the formula for $\theta(c)$ on p. 294. The coefficient of $X^2$ should be $(c^4-c^2) 12$, not $(c^4+2c^2-3c) 24$. Although very embarrassing, the error is inconsequential in the sense that there was no need to display the coefficient of $X^2$ in the first place. Preprints This list is confined to papers which have not yet appeared (e. g. [1] and [2]), or will never appear (e. g. [3]), or have appeared in journals which may be difficult to find (e. g. [4] and [5]). All of the listed papers are readable with Adobe Acrobat Reader: 1. Root numbers of semistable elliptic curves in division towers. 2. Serge Lang. 3. Universal deformation rings and universal elliptic curves. 4. Galois representations in Mordell-Weil groups of elliptic curves. 5. Homomorphisms into groups of formal power series.
Ren Xiumin
Shandong University. Additive problems; Exponential sums over prime variables.
third Xiumin Ren Address Department of Economics, Shandong University Jinan, Shandong 250100 P.R. China Research Interests Additive problems Exponential sums over prime variables Publications [4] The exceptional set in Roth's theorem concerning a cube and three cubes of primes, Q. J. Math. 52 (2001), no. 1, 107-126. [3] Density of integers that are the sum of four cubes of primes, Chinese Ann. Math. Ser. B 22 (2001), no. 2, 233-242. [2] The Waring-Goldbach problem for cubes, Acta Arith. 94 (2000), no. 3, 287-301. [1] Newton-like methods for determining zeros of nonsmooth order-convex operators, (Chinese) Numer. Math. J. Chinese Univ. 15 (1993), no. 3, 232-239.
Rudnick, Zeev
Tel-Aviv University. Number theory; quantum chaos.
Zeev Rudnick's home page Zeev Rudnick Professor of Mathematics at Tel-Aviv University . Major interests Number Theory Mathematical Physics, especially "Quantum Chaos" Publications and Preprints Curriculum Vitae teaching in 2005 6: Fall Introduction to Number Theory , Tuesday 8-10 , Wednesday 10-12, Shenkar 204 . Linear algebra for engineers , Monday 14-16, Wednesday 14-17, Wolfson 238. Teaching assistant: Mr. Frol Zapolsky Recitation sessions: Wednesday 1012, Wolfson 118, THursday 13-15 Wolfson 108 Spring Graduate seminar in number theory Past Courses Summer schools Equidistribution in Number Theory , sponsored by NATO, July 11-22, 2005. Summer school on on the Rieman zeta function and Random Matrix Theory Oberwolfach October 15-21, 2000. Office address: Schrieber Building, Room 316, School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel. Phone: +972-3-640-7806, Departmental Fax: +972-3-640-9357, Personal Fax +972-3-6405374 email: rudnick at math tau ac il
Richert, Hans-Egon
Obituary from Universitaet Ulm.
Died: Prof. Dr. Hans-Egon Richert University of Ulm Faculty of Mathematics and Economics Faculty Home Page Infos Forum zu Wirtschaftsmathematik Press Releases Links Mathematics Local Webservers Died: Prof. Dr. Hans-Egon Richert Deutsch On the 25th of November 1993, Professor Dr. Hans-Egon Richert died in Blaustein near Ulm, Germany, after a long and severe illness. Richert held a chair of Mathematics at the University of Ulm from 1972 until his retirement as an emeritus professor in 1991. Richert was born 1924 in Hamburg and was raised there. He had to complete high school at a private institution after being expelled from the public school in the period of the Third Reich for "anglophile leanings". In 1946, at last back in Hamburg after the war and military service, he could begin his studies of mathematics. He obtained his diploma after eight terms and his PhD only one year later. When his mentor, Professor Max Deuring, accepted a position in Gttingen, the young Richert joined him as an assistant and obtained the venia legendi there in 1954. Soon after he was put in charge of one of the best mathematical libraries in Germany. After holding a temporary chair in Gttingen he was offered a newly created chair at the University of Marburg. In that time of vigorous development of the entire university system, Richert contributed in an essential way to shaping the Marburg Mathematical Institute, and, of course, he devoted his special love and attention to the library. From 1969 on, emotion held sway over reason in daily academic life in German universities, and especially so in Marburg. He was therefore pleased to accept in 1972 a chair at the young University of Ulm. His professorship here was the second one in the Mathematics Department, after that of Alexander Peyerimhoff. There was again much need for development. Science had priority for Richert, teaching as well as research. Those who knew him from committee meetings recall that Richert spoke only when it was really necessary. He used to cut short a tedious discussion with a few well chosen and constructive - but never offensive - words. He also participated in reasonable administrative activities: in 1974 75 he served his university as Prorektor, then as a member of the unbeloved room allocation board, which in effect had to allocate shortages, and he acted for almost twenty years as chairman of the examination committee, an office that he administered unbureaucratically and always in the interest of the students. Richert's field of research was Analytic Number Theory. He made important contributions to additive prime number theory, Dirichlet series, Riesz summability, the multiplicative analog of the Erds-Fuchs theorem, estimates of the number of non-isomorphic abelian groups and bounds for exponential sums for use, e. g. in estimating the error term of the prime number theorem. From about 1965 on he focussed his research increasingly on sieve methods. Among other things he put the proof of Chen's p+P_2 theorem into readable form. An intensive research collaboration developed between Richert and Heini Halberstam, motivated by their common interest in sieves, and lasted for the rest of his life. The monograph on Sieve Methods that they coauthored immediately became the indispensable basis for research of many number theorists. Also, Richert's name was long associated with the best estimate for the Dirichlet divisor problem. For many years he was one of the chairmen of the Oberwolfach meetings on Analytic Number Theory. The very high esteem he enjoyed in the mathematical community is reflected by the many invitations he received from mathematical institutions abroad, among others the University of Illinois at Urbana and the Tata Institute in Bombay. His life was not confined to mathematics: Richert was also a stimulating conversational partner on many different subjects. He enjoyed exploring foreign countries and keeping records of his trips on film and tape, a pursuit that he followed with the same intensity as his science whenever time allowed. In 1991 Professor Richert had to retire from his strenuous teaching duties. It is sad that he was not granted the long and fruitful period of retirement that he was looking forward to. With the passing of Hans-Egon Richert we lose a treasured colleague and a researcher of international reputation. Ulrike Vorhauer and Eduard Wirsing Web Administration , last update on September 12th, 2005
Rio, Anna
Universitat Politcnica de Catalunya. Galois representations, elliptic curves, modular forms.
Anna Rio (Homepage) Anna Rio Departament de Matemtica Aplicada II Universitat Politcnica de Catalunya Jordi Girona, 1-3 08034- Barcelona (Spain) Phone: + 34 - 93 413 76 88 Fax: + 34 - 93 413 77 01 mail: enviar missatge Docncia 05-06 (Q1): lgebra 1 (Diplomatura d'Estadstica) Informaci Research Interests: Number Theory. Galois representations, elliptic curves, modular forms Papers Some Links Department Home Page
Robinson, Margaret M.
Mount Holyoke. Igusa local zeta functions.
Margaret M. Robinson Prof. Margaret M. Robinson Office: Clapp 402A Telephone: 413-538-2394 Fax: 413-538-3035 E-mail: robinson@mtholyoke.edu Current Courses Old Courses Some Papers Algebraic identities useful in the computation of the Igusa local zeta function", Algebraic Geometry and Number Theory, A. Adolphson, S. Sperber, and M. Tretkoff (editors), AMS Contemporary Mathematics Series, 133, 1992, 171-4. The Igusa local zeta function associated with the singular cases of the determinant and the Pfaffian, J. of Number Theory, 57 (1996), no. 2, 385-408. The Igusa local zeta function of a non-trival character associated to the singular Jordan algebras, Proc. Amer. Math. Soc. 124 (1996), no. 9, 2655-60. On the tabletop improvement experiments of Japan, Production and Operations Management, 3, No. 3, Summer 1994, joint with Alan G. Robinson. Laboratories in Mathematical Experimentation: A Bridge to Higher Mathematics (Projects for a sophomore course in mathematical investigations; written by the members of the Department of Mathematics and Statistics, Mount Holyoke College and published by Springer in April 1997) Mount Holyoke College Summer Research Institute" in Women in Mathematics: Scaling the Heights, Deborah Nolan (editor), MAA Notes 46 (1997), 113-6. An Introduction to Local Zeta Functions", a review of Jun-ichi Igusa's new book in Bulletin (New Series) of the American Mathematical Society 38, No. 2, (2000) 221-227. Igusa Local Zeta Functions of Elliptic Curves, Mathematics of Computation, 71 (2001), no. 238, 815-823, (joint with Prof. Diane Meuser, Boston University). Research Experiences for Undergraduates (REU) Projects P-adic analysis and computing the Igusa local zeta function for irreducible curves (1992) P-adic analysis and the Igusa local zeta function for reducible curves and for surfaces with bad reduction modulo p (1995) The Igusa local zeta function for elliptic curves and a related Poincare Series (1997) The Igusa local zeta function for elliptic curves using Tate's Algorithm (1999) Number Theory (2002) Number Theory (2005) Other interesting mathematics links Page maintained by robinson@mtholyoke.edu
Quer, Jordi
Universitat Politcnica de Catalunya. Number theory and arithmetic geometry.
Jordi Quer Jordi Quer Universitat Politcnica de Catalunya Departament Matemtica Aplicada II Campus Nord, Edifici Omega, Despatx 438 Jordi Girona, 1-3 08034 - Barcelona, Spain Research Docncia Tel: +34-934137974 Email address: Jordi.Quer, at upc.edu
Queme, Roland
Algebraic number theory.
Roland Queme Home Page Roland Qume 13 Avenue du chteau d'eau 31490 Brax France roland.queme@wanadoo.fr * home page: http: roland.queme.free.fr * Last update : 2005 feb 07 Private domain of interest : Algebraic Number Theory : Geometry of Numbers Diophantine Approximation of algebraic numbers Cyclotomic fields and Fermat's Last Theorem Prepublications : pi-adic approach of p-class group and unit group of p-cyclotomic fields - Version 2.0 2005 feb 04 preprint arXiv.org at http: arxiv.org section math, keyword author: queme manuscrit math.NT 0407430 Some congruences on prime factors of class number of finite algebraic extensions K Q- Version2.0 2003 apr 25 preprint arXiv.org at http: arxiv.org section math, keyword author: queme manuscrit math.NT 0304405 A classical approach on cyclotomic fields and Fermat-Wiles theorem Version 1.2 2002 oct 31 preprint arXiv.org at http: arxiv.org section math, keyword author: queme manuscrit math.NT 0211467 * Some Publications : A computer algorithm for finding new euclidean number fields, Journal de Thorie des Nombres de Bordeaux, 10, 1998, pp 33-48 (I have found 1205 new euclidean number fields in the degrees 4 ,5,6 with this algorithm, more than all the euclidean fields known in all degree when I wrote this paper and my C++ program). On diophantine approximation by algebraic numbers of a number field, a new generalization of Dirichlet approximation theorem, Astrique 198-199-200, 1991, p. 273-283 Gerhard Nicklasch Roland Queme, An improvement of Lenstra's criterion for euclidean number fields : the totally real case : Acta Arithmetica LVIII.2, 1991, p. 157-168. Relations d'ingalit effective en thorie algbrique des nombres, Sminaire de thorie des nombres de Bordeaux, anne 1987-1988, expos n 19. Majorations du nombre de classes, C.R. Acad. Sci . Paris, t. 307, Srie I, 1988, p. 199-122. Une relation d'ingalit entre discriminant, nombre de classes et rgulateurs des corps de nombres, C.R. Acad. Sci . Paris, t. 306 Srie I, 1988, p 5-10. These 3me Cycle Universit Paris Sud Orsay (France), on euclidean number fields , with Professeur Pierre Samuel, 1982: "Etude des Algorithmes de divisibilit et de la factorisation des anneaux et monoides de fractions" * Links to other sites : Number Theory Web * Last update : 2005 feb 07
Papaioannou, Thanos
Harvard University. Elliptic Curves, Algebraic Geometry, Class Field Theory and Algebraic Topology.
The Homepage of Thanos Papaioannou MATHEMATICAL MISCELLANY T HANOS (A THANASIOS ) P APAIOANNOU All art constantly aspires to the condition of Number Theory. Walter Pater; quotation slightly vandalised. Welcome to my pompous page; I am a maths student at Harvard. You may find some of my notes and writings below. E XPOSITORY PAPERS Grothendieck sheaf duality . Paper written for Jay Pottharst's and Cameron Freer's Sheaves in Logic and Geometry tutorial, spring 2005. It discusses Hartshorne's theorem on the duality of quasi-coherent sheaves. Unfinished! Cobordism and the Thom spectrum construction . Paper written for Dylan Thurston's Algebraic Topology class, fall 2004. It discusses cobordism and the Thom-Pontryagin theorem. An algebraic approach to the Riemann-Roch theorem and the arithmetic theory of function fields . Paper written for Deepee Khosla's Riemann Surfaces and Algebraic Curves tutorial, summer 2004. It follows a nave algebraic route to the Riemann-Roch theorem for algebraic curves. P UBLIC NOTES Mathematics 55 . Section handouts on various topics, including category theory, the topology of projective space, commutative and homological algebra, sheaves, sheaf cohomology and deRham's theorem. Motives and cohomology . Schedule of lectures and bibliography of an informal seminar on motives and cohomology. A concise introduction to Lubin-Tate theory . Lecture notes for a mini-course given to PROMYS counsellors, summer 2005. Unfinished! P RIVATE NOTES Technique of descent and existence theorems in algebraic geometry . Translation of Grothendieck's Bourbaki expos 190, which summarises chapters VI and VIII of SGA 1 and also gives an elegant, geometric proof of Hilbertsatz 90. Unfinished! Algebraic number theory . Lecture notes from Richard Taylor's Algebraic Number Theory class, 2004-2005. I have temporarily restricted public access to this file. Unfinished! Number theory in function fields: Dirichlet's theorem about primes in arithmetic progressions . Lecture notes for a talk at the Harvard Math Table on 20th April 2003. R ATHER PERSONAL LINKS Table of contents of EGA I-IV . My view of the world . My schedule . Miltos Sahtouris . Miltos Sahtouris is a dark Greek surrealist poet; I have collected translations of some of his work in the above link. (You might also wish to download a pdf version of that page.) C ONTACT Athanasios Papaioannou 492 Cabot House Mail Center Harvard University Cambridge, MA 02138 O, the marvels of electronic mail .
Parsell, Scott
Butler University. Exponential sums; Hardy-Littlewood method; Diophantine problems. Papers, thesis.
Scott Parsell Scott Parsell Jordan Hall 270B (317) 940-3239 sparsell@butler.edu Department of Mathematics Butler University Indianapolis , IN 46208 I was born and raised in Akron, Ohio, where I graduated from Walsh Jesuit High School in 1990. I completed my undergraduate work at MIT in 1994 and obtained my Ph. D. in Mathematics at the University of Michigan in 1999 under the direction of Trevor Wooley . I was a visiting assistant professor in the Math Department at Texas AM University from 1999-2001, and I was an NSF Postdoctoral Fellow in Mathematics at Penn State University from 2001-2004. I am currently an assistant professor of mathematics at Butler University in Indianapolis . This page is currently under construction. Fall 2005 course materials for MA 106 (Calculus I) and MA 326 (Real Analysis) are posted on Blackboard. Wedding Page
Pierce, Lillian
Princeton University. Analysis and number theory. Publications, junior, senior and MSc theses.
Lillian Pierce - Home Page - Princeton Lillian Pierce Graduate Student Department of Mathematics Fine Hall Princeton University Princeton, NJ 08544 lbpierce_at_princeton_dot_edu Research Interests Analysis, number theory. Publications The 3-Part of Class Numbers of Quadratic Fields J. London Math. Soc., in press (pdf) A Bound for the 3-Part of Class Numbers of Quadratic Fields by Means of the Square Sieve Forum Math., in press (pdf) Theses The 3-Part of Class Numbers of Quadratic Fields MSc Thesis, Oxford University, 2004 (pdf) Advisor: D.R. Heath-Brown This original thesis gives the first nontrivial bounds for the 3-part of class numbers of quadratic fields, using techniques of analytic number theory such as mean values of exponential sums, the square sieve, and the q-analogue of van der Corput's method. The Pair Correlation of the Zeroes of the Riemann Zeta Function Senior Thesis, Princeton University, 2002 (pdf) Advisor: E.M. Stein An expository thesis giving a proof of Montgomery's original theorem, the derivation of the GUE pair correlation function, and an examination of the computational results of Odlyzko. Hardy Functions Junior Paper, Princeton University, 2001 (pdf) Advisor: E.M. Stein An expository paper giving a proof of the Paley-Wiener theorem and applications of Hardy functions as signal filters.
Prasad, Dipendra
Tata Institute for Fundamental Research. Algebraic number theory, Automorphic forms, Representation theory. Publications.
D. Prasad Dipendra Prasad Email: dprasad@math.tifr.res.in Professor of Mathematics. PhD from Harvard University, 1989. Mathematical Interest: Algebraic number theory, Automorphic forms, Representation theory. [ List of Publications ] [ Description of Work ] [ Professional Recognition ] [ Professional Experience ] List of Publications Papers in Journals Trilinear forms for representations of GL(2) and local epsilon factors, Compositio Math 75, 1-46 (1990). [ TEX file ] [ DVI file ] (With B.H. Gross) Test Vectors for linear forms, Maths Annalen 291, 343-355 (1991). PDF file . Invariant linear forms for representations of GL(2) over a local field, American J. of Maths 114, 1317-1363 (1992). [ TEX file ] [ DVI file ] (With B.H. Gross) On the decomposition of a representation of SO(n) when restricted to SO(n-1), Canadian J. of Maths 44, 974-1002 (1992). [ TEX file ] [ DVI file ] On the decomposition of a representation of GL(3) restricted to GL(2), Duke J. of Maths 69, 167-177 (1993) PDF file . Bezout's theorem for simple abelian varieties, Expositiones Math. 11, 465-467 (1993). On the local Howe duality correspondence, IMRN, No. 11, 279-287 (1993). [ PDF file ] (With B.H. Gross) On irreducible representations of SO(2n+1)xSO(2m), Canadian J. of Maths, vol 46(5), 930-950 (1994). On an extension of a theorem of Tunnell, Compositio Math., 94, 19-28(1994). (With D. Ramakrishnan) Lifting orthogonal representations to spin groups and local root numbers, Proc. of the Indian Acad. of Science, vol 105, 259-267 (1995). [ TEX file ] [ DVI file ] Some applications of seesaw duality to branching laws, Maths Annalen, vol. 304, 1-20 (1996). [ TEX file ] [ DVI file ] [ PDF file ] (With C.S. Khare) Extending local representations to global representations, Kyoto J. of Maths, vol 36, 471-480 (1996). [ TEX file ] [ DVI file ] On the self-dual representations of finite groups of Lie type, J. of Algebra, vol 210, 298-310 (1998). [ TEX file ] [ DVI file ] Some remarks on representations of a division algebra and of Galois groups of local fields, J. of Number Theory, vol 74, 73-97 (1999). [ TEX file ] [ DVI file ] Distinguished representations for quadratic extensions, Compositio Math., vol. 119(3), 343-354 (1999). [ PDF file ] (with D. Ramakrishnan) On the global root numbers of $GL(n) \times GL(m)$, Proceedings of Symposia in Pure Maths of the AMS, vol. 66, 311-330, (1999). [ TEX file ] [ DVI file ] On the self-dual representations of $p$-adic groups, IMRN vol. 8, 443-452 (1999). [ TEX file ] [ DVI file ] [ PDF file ] (With Kumar Murty) Tate cycles on a product of two Hilbert Modular Surfaces, J. of Number Theory, vol. 80, 25-43 (2000). [ TEX file ] [ DVI file ] Theta correspondence for Unitary groups, Pacific J. of Maths vol 194, no. 2, 427-438 (2000). [ TEX file ] [ DVI file ] (with A. Raghuram) Kirillov theory of $GL_2(D)$ where $D$ is a division algebra over a non-Archimedean local field, Duke J. of Math, vol 104, no. 1, 19-44 (2000). [ DVI file ] Comparison of germ expansion for inner forms of $GL_n$, Manuscripta Mathematicae, vol 102, 263-268 (2000). [ TEX file ] [ DVI file ] The space of degenerate Whittaker models for general linear groups over finite fields, IMRN, vol 11, 579-595 (2000). [ TEX file ] [ DVI file ] (With C. Khare) On the Steinitz module and capitulation of ideals, Nagoya Math. J.vol. 160, 1-15 (2000). [ TEX file ] [ DVI file ] (with C.S.Yogananda) Bounding the torsion in CM elliptic curves, Comptes Rendus Mathematiques Mathematical Reports of the Academy of Sciences, Canada , vol. 23, 1-5 (2001). [ TEX file ] [ DVI file ] On a conjecture of Jacquet about distinguished representations of $GL_n$, Duke J. of Math, vol. 109, 67-78 (2001). [ DVI file ] Locally algebraic representations of $p$-adic groups, appendix to the paper by P.Schneider and J.Teitelbaum, $U({\frak g})$-finite locally analytic representations, (Electronic Journal) Representation Theory ,5, 111-128 (2001). [ TEX file ] [ DVI file ] (with Nilabh Sanat)} On the restriction of cuspidal representations to unipotent elements, Math. Proceedings of Cambridge Phil. Society 132, No. 1, 35-56 (2002). [ PDF file ] (with CS Rajan)} On an Archimedean analogue of Tate's conjecture, J. of Number Theory, vol. 99 (2003), 180-184. [ TEX file ] [ DVI file ] On an analogue of a conjecture of Mazur: A question in Diophantine approximation, Contributions to automorphic forms, geometry, and number theory, 699--709, Johns Hopkins Univ. Press, Baltimore, MD, 2004. [ PDF file ] (with C. Khare) Reduction of homomorphisms mod $p$, and algebraicity, J. of Number Theory 105, 322--332 (2004). [ TEX file ] [ DVI file ] (with SO Juriaans and IBS Passi) Hyperbolic Unit Groups, Proc. of the AMS 133, (2005) no. 2, 415-423. [ TEX file ] [ DVI file ] (with UK Anandavardhanan) Distinguished representations for $SL(2)$, Math. Res. Letters 10, 867--878 (2003). [ TEX file ] [ PDF file ] (with Jeffrey D. Adler) On certain mulitplicity one theorems, to appear in Israel J. of Mathematics . [ TEX file ][ PS file ][ PDF file ] (with Dinakar Ramakrishnan) On the self-dual representations of division algebras over local fields, to appear. [ TEX file ][ DVI file ][ PDF file ] (with UK Anandavardhanan) On the SL(2) period integral, to appear in American J. of Mathematics . [ TEX file ][ DVI file ][ PDF file ] Relating invariant linear form and local epsilon factors via global methods. [ PDF file ] Papers in Conference Proceedings Weil representation, Howe duality, and the theta correspondence, AMS and CRM proceeding and lecture notes, 105-126 (1993). [ TEX file ] [ DVI file ] Ribet's Theorem: Shimura-Taniyama-Weil implies Fermat, Proceedings of the seminar on Fermat's Last Theorem at Fields Institute, edited by V. Kumar Murty, CMS Conference Proceedings, vol. 17, 155-177 (1995). A brief survey on the Theta correspondence, Proceedings of the Trichy Conference edited by K. Murty and M. Waldschmidt, Contemporary Maths, AMS, vol. 210, 171-193 (1997). [ TEX file ] [ DVI file ] (with C.S.Yogananda) A report on Artin's holomorphy conjecture, in the volume on Number Theory, edited by R.P.Bambah, V.C.Dumir, and R.J.Hans-Gill, Hindustan Book Agency, (1999) 301-314. [ TEX file ] [ DVI file ] The space of degenerate Whittaker Models for $GL_4$ over $p$-adic fields, Proceedings of the TIFR conference on Automorphic Forms, AMS (2001). [ TEX file ] [ DVI file ] Unpublished Papers Distinguished representations for quadratic extension of a finite field. [ TEX file ] [ DVI file ] Contributions to Algebraic number theory from India since Independence, unpublished. [ TEX file ] [ DVI file ] [ PDF file ] Unpublished Lecture Notes Lectures on Algebraic number theory. [ TEX file ] [ DVI file ] Lectures on Algebraic Groups. [ TEX file ] [ DVI file ] (with A. Raghuram) Representation theory of $GL(n)$ over non-Archimedean local fields, lecture notes for a workshop at ICTP, Italy (2001). [ TEX file ] [ DVI file ] A Brief Description of Work so far Branching Laws for representations of Real and p-adic groups: Many problems in representation theory involve understanding how a representation of a group decomposes when restricted to a subgroup. Situations which involve multiplicity one phenomenon in which either the trivial representation, or some other representation of the subgroup appears with multiplicity at most one is specially useful. To cite a few examples, the theory of spherical functions and Whittaker models depends on such a multiplicity one phenomenon. The Clebsch-Gordon theorem about tensor product of representations of SU(2) has been very useful both in Physics and Mathematics. Many of my initial papers have been about finding such multiplicity one situations for infinite dimensional representations of real and $p$-adic groups. The results are expressed in terms of the arithmetic information which goes in parameterising representations, the so called Langlands parameters . In particular, the Clebsch-Gordon theorem was generalised by me for infinite dimensional representations of real and $p$-adic GL(2). Several papers, some written in collaboration with B.H.Gross, point out to the importance of the so called epsilon factors in these branching laws. The papers [1], [2], [3], [4], [5], [9], [11], [14] belong to this theme. These works have implication for the global theory of automorphic forms. There are many parallels between global period integrals, expressed in many situations as special value of $L$-functions, and local branching laws expressed in terms of epsilon factors. The paper [15] studies the question of when a representation of $G(K)$ has a $G(k)$-invariant vector for $K$ a quadratic extension of $k$ for $k$ either a finite or a $p$-adic field. In the $p$-adic case, this was done only for division algebras in [15]. I have used the methods of this paper to prove a conjecture of Jacquet about distinguished representations of $GL_n$ and $U_n$ in the case when $K$ is a unramified quadratic extension of $k$ in [25]. Lusztig has followed up the theme of [15] in his recent paper in the Electronic J. of the AMS. I have just finished writing a paper [33] with Jeff. Adler in which we prove several multiplicity 1 theorems; in particular we show that an irreducible representation of $GSp(2n)$ when restricted to $Sp(2n)$ decomposes with mutiplicity 1 for $p$-adic fields. Weil Representations: Generalising the classical construction of theta functions, Weil representations provide one of the few general methods of constructing representations of groups over real and $p$-adic groups, as well as automorphic forms. The relation of this construction of representations to the Langlands parametrisation is still not fully understood. I have written two papers dealing with this question in which I refine some conjectures of Jeff Adams on the Langlands parameters of representations obtained via the Weil construction, thus making rather precise conjectures about the behaviour of the theta correspondence for groups of similar size. I have also done some work on the $K$-type of the Weil representation, and also on the character formula for the Weil representation. Papers [7], [19] as well as the expository paper [38] containing some new results too, belong to this theme. Representations of division algebras and of Galois groups of local fields: Generalising local class field theory, Langlands has conjectured a correspondence between irreducible representations of $GL(n)$ or of a division algebra of index $n$ to $n$ dimensional representations of the Galois group of the local field. This correspondence has recently been established by Harris, Taylor and Henniart. The correspondence preserves self-dual representations. Self-dual representations are of two kinds: symplectic and orthogonal. The question is: how does the Langlands correspondence behave on these two kinds of self-dual representations. Based on considerations of Poincare duality on the middle dimensional cohomology of a certain rigid analytic space, Dinakar Ramakrishnan and I conjecture that a representation of division algebra is orthogonal if and only if the associated representation of the Galois group is symplectic. The conjecture was made in [10]. The paper [14] was also motivated by its consideration. In [33] with Ramakrishnan we show how this conjecture is a consequence of `functoriality', and since the functorial lift between classical groups and $GL(n)$ is now known in many cases, we are able to prove the conjecture in [34] for those cases when the parameter is symplectic. Self-dual representations of finite and $p$-adic groups : For a compact connected Lie group it is a theorem due to Malcev that an irreducible, self-dual representation carries an invariant symmetic or skew-symmetric bilinear form depending on the action of a certain element in the center of the group. We have generalised this result to finite groups of Lie type in [13] and to $p$-adic groups in [17]. These results are, however, proved only for generic representations. These results provide an answer to a question raised by Serre. Kirillov Whittaker models : In the work [20] done with A. Raghuram, we develop Kirillov theory for irreducible admissible representations of $GL_2(D)$ where $D$ is a division algebra over a non-Archimedean local field. This work is in close analogy with the work of Jacquet-Langlands done in the case when $D$ is a field, and realises any irreducible admissible representation of $GL_2(D)$ on a space of functions of $D^*$ with values in what may be called the space of degenerate Whittaker models which is the largest quotient of the representation on which the unipotent radical of the minimal parabolic which is isomorphic to $D$ acts via a non-trivial character of $D$. Paper [22] studies this space of degenerate Whittaker models for finite fields obtaining a rather pretty result about the space of degenerate Whittaker model for a cuspidal representation of $GL_{2n}({\Bbb F})$ with respect to the $(n,n)$ parabolic with unipotent radical $M_n({\Bbb F})$. In paper [40] in the conference proceedings of a conference at the Tata Institute on Automorphic forms, I elaborate on a conjecture with B. Gross which gives a very precise structure for the space of degenerate Whittaker models on $GL_2(D)$ when $D$ is a quaternion division algebra. There is also a proposal in this paper to interpret triple product epsilon factors (for $GL(2)$) in terms of intertwining operators. Modular forms: There is a well known theorem of Deligne about estimates on the Fourier coefficients of modular forms. In the paper [12] with C. Khare, we study whether the converse is true, i.e. if given finitely many algebraic integers satisfying Deligne bounds, there exists an eigenform of Hecke operators with these algebraic integers as Fourier coefficients. One simple case of this problem is solved by an application of Wiles's theorem about the Shimura-Taniyama conjecture. Tate Cycles: In paper [18] with Kumar Murty, we parametrise Tate cycles on products of two Hilbert modular surfaces in terms of Hilbert modular forms, including the precise information about the field of rationality. Representations of finite groups of Lie type: I have worked on some aspects of representation theory of finite groups of Lie type with my student Nilabh Sanat, and we have written a paper [27] together. This paper decomposes an irreducible cuspidal representation of a classical group restricted to its maximal unipotent subgroup as an alternating sum of certain explicit unipotent representations. Other works : I have a short note [6] in which I give a proof of the analogue of Bezout's theorem for abelian varieties: any two subvarieties of complementary dimensions in a simple abelian variety intersect. When the paper was written, I did not know that the theorem was due to W. Barth, but the proof presented in [6] was different anyway. L. Merel has proved an important theorem stating that the order of torsion on elliptic curves over a number field are bounded independent of the elliptic curve and the field, and depends only on the degree of the field. However, there are still no good bounds. In an attempt to see what might be the best bound, in a note with Yogananda [24], we estimate the bounds on torsion on CM elliptic curves. I have made an analogue of a conjecture of Mazur on the density of rational points in the Euclidean topology on an Abelian variety to certain tori (isomorphic to $({\Bbb S}^1)^n$ but non-algebraic!), and proved it using the Schanuel conjecture in [29]. In a paper with C. Khare [30] we prove that an abstract homomorphism between the Mordell-Weil group of abelian varieties over a number field which respects reduction mod $p$, in fact arises from homomorphism of abelian varieties. The paper [28] written with CS Rajan is a re-look at Sunada's theorem about isospectral Riemannian manifolds where we deduce it as a consequence of a simple lemma in group theory. In this paper we also conjecture, and verify in several cases, that the Jacobians of two Riemann surfaces with the same spectrum for Laplacian are isogenous (after an extension of the base field), and propose this as an Archimedean analogue of Tate's conjecture. I have written some survey papers, of which [37], [38] might have some results which may not be found elsewhere. Professional Recognition, Awards, Fellowships received : 1. Sloan Fellowship at Harvard University 1988-89. 2. NSERC fellowship of the Canadian Government, 1993. 3. BM Birla Prize in Mathematics for the year 1994. 4. Elected fellow of the Indian Academy of Science in 1995. 5. Elected fellow of the National Academy of Science, India in 1997. 6. Swarna Jayanti Fellowship for Mathematics awarded in the year 98-99 for 5 years. 7. Shanti-Swarup Bhatnagar Award for Mathematical Sciences for the year 2002. Professional Experience: Research Scholar TIFR, Bombay 1980-1985 Graduate student Harvard University 1985-19 89 Research Assistant TIFR, Bombay 1989-1990 Fellow TIFR, Bombay 1990-1993 Reader TIFR, Bombay 1993-1997 Associate Professor Mehta Research Institute 1994- 1997 Professor Mehta Research Institute 1997- member Institute for Advanced Study Princeton, 1992-93 visitor University of Toronto 1993 visitor MSRI, Berkeley Spring 1995 visitor Harvard University Spring 1997 Visiting Associate Professor University of Chicago Spring 1998 Visiting Professor University of Chicago Spring 2000. Visiting Professor Cal. Tech. Spring 2003 Back to School of Mathematics, TIFR. Last modified: Tue Nov 4 17:30:44 IST 2003
Plater, Andrew J.
University of Cambridge. Contact information.
Dr A.J. Plater Department of Pure Mathematics and Mathematical Statistics DPMMS People Dr A.J. Plater Dr A.J. Plater Title:Director of Studies in Mathematics Email: A.J.Plater@dpmms.cam.ac.uk College:Hughes Hall Room: C0.01 Tel: +44 1223 339795 Research Interests: Number Theory 2003-2005 Department of Pure Mathematics and Mathematical Statistics, University of Cambridge Information provided by webmaster@dpmms.cam.ac.uk
Pomerance, Carl
Dartmouth College. Analytic and computational number theory. Publications.
Carl Pomerance Carl Pomerance Phone: (603) 646-6236 Dept. Fax: (603) 646-1312 Office: 102 Choate House Office Hours: Tuesday, Wednesday, Thursday 9:00 - 10:00 AM Email: carl.pomerance@dartmouth.edu US Mail: Department of Mathematics Dartmouth College Hanover, NH 03755-3551 (603) 646-2415 Course proposal for Math 75 Brief CV List of Papers Odd perfect numbers are divisible by at least seven distinct primes, C. Pomerance, Acta Arith. 25 (1974), 265-300. On Carmichael's conjecture , C. Pomerance, Proc. Amer. Math. Soc. 43 (1974), 297-298. A search for elliptic curves with large rank , D.E. Penney and C. Pomerance, Math. Comp. 28 (1974), 851-853. 714 and 715, C. Nelson, D.E. Penney and C. Pomerance, J. Rec. Math. 7 (1974), 87-89. Three elliptic curves with rank at least seven , D.E. Penney and C. Pomerance, Math. Comp. 29 (1975), 965-967. The second largest prime factor of an odd perfect number , C. Pomerance, Math. Comp. 29 (1975), 914-921. On the congruences (n) a (mod n) and n a (mod (n)), C. Pomerance, Acta Arith. 26 (1975), 265-272. On an interesting property of 112359550561797752809, J.L. Hunsucker and C. Pomerance, Fibonacci Quarterly 13 (1975), 331-333. There are no odd super perfect numbers less than 7 x 10^{24}, J.L. Hunsucker and C. Pomerance, Indian J. Math. 17 (1975), 107-120. Some new results on odd perfect numbers , G.G. Dandapat, J.L. Hunsucker and C. Pomerance, Pacific J. Math. 57 (1975), 359-364. On multiply perfect numbers with a special property , C. Pomerance, Pacific J. Math. 57 (1975), 511-517. On composite n for which (n)|n-1, I, C. Pomerance, Acta Arith. 28 (1976), 387-389. Multiply perfect numbers, Mersenne primes and effective computability , C. Pomerance, Math. Ann. 226 (1977), 195-206. On a tiling problem of R. B. Eggleton , C. Pomerance, Discrete Math. 18 (1977), 63-70. On composite n for which (n)|n-1, II , C. Pomerance, Pacific J. Math. 69 (1977), 177-186. On the distribution of amicable numbers, C. Pomerance, J. reine angew. Math. 293 294 (1977), 217-222. On the largest prime factors of n and n+1 , P. Erds and C. Pomerance, Aequationes Math. 17 (1978), 311-321. On a class of relatively prime sequences , P. Erds, D.E. Penney and C. Pomerance, J. Number Theory 10 (1978), 451-474. The prime number graph , C. Pomerance, Math. Comp. 33 (1979), 399-408. On a problem of Evelyn - Linfoot and Page in additive number theory, C. Pomerance and D. Suryanarayana, Publ. Math. Debrecen 26 (1979), 237-244. Nearly parallel vectors, H.G. Diamond and C. Pomerance, Mathematika 26 (1979), 258-268. Some number theoretic matching problems, C. Pomerance, Proceedings of the Queen's Number Theory Conference, P. Ribenboim, ed., Queen's Papers in Pure and Applied Mathematics, No. 54, Kingston, Canada, 1979, 237-247. Collinear subsets of lattice point sequences - an analogue of Szemerdi's theorem , C. Pomerance, J. Combinatorial Theory (A) 28 (1980), 140-149. A note on the least prime in an arithmetic progression , C. Pomerance, J. Number Theory 12 (1980), 218-223. The pseudoprimes to 25 x 10^9 , C. Pomerance, J.L. Selfridge and S.S. Wagstaff, Jr., Math. Comp. 35 (1980), 1003-1026. Matching the natural numbers up to n with distinct multiples in another interval , P. Erds and C. Pomerance, Nederl. Akad. Wetensch. Proc. Ser. A 83 (1980), 147-161. Proof of D.J. Newman's coprime mapping conjecture, C. Pomerance and J.L. Selfridge, Mathematika 27 (1980), 69-83. Popular values of Euler's function, C. Pomerance, Mathematika 27 (1980), 84-89. Sets on which an entire function is determined by its range , H.G. Diamond, C. Pomerance and L. Rubel, Math. Z. 176 (1981), 383-398. On the distribution of amicable numbers, II, C. Pomerance, J. reine angew. Math. 325 (1981), 183-188. The arithmetic mean of the divisors of an integer, P.T. Bateman, P. Erds, C. Pomerance and E.G. Straus, Analytic Number Theory Proceedings, Philadelphia 1980, M. I. Knopp, ed., Lecture Notes in Math. 899 (1981), 197-220. On the distribution of pseudoprimes , C. Pomerance, Math. Comp. 37 (1981), 587-593. Recent results in primality testing, C. Pomerance, Math. Intelligencer 3 (1981), 97-105. A new lower bound for the pseudoprime counting function, C. Pomerance, Illinois J. Math. 26 (1982), 4-9. The search for prime numbers, C. Pomerance, Scientific American 247, No. 6 (1982), 136-144. Analysis and comparison of some integer factoring algorithms , C. Pomerance, Computational Methods in Number Theory, Part I, H.W. Lenstra, Jr. and R. Tijdeman, eds., Math. Centre Tract 154, Amsterdam, 1982, 89-139. On distinguishing prime numbers from composite numbers , L.M. Adleman, C. Pomerance and R.S. Rumely, Annals Math. 117 (1983), 173-206. An analogue of Grimm's problem of finding distinct prime factors of consecutive integers, P. Erds and C. Pomerance, Utilitas Math. 24 (1983), 45-65. On a problem of Oppenheim concerning `Factorisatio Numerorum' , E.R. Canfield, P. Erds and C. Pomerance, J. Number Theory 17 (1983), 1-28. Implementation of the continued fraction integer factoring algorithm, C. Pomerance and S.S. Wagstaff, Jr., Congressus Numerantium 37 (1983), 99-117. On the longest simple path in the divisor graph, C. Pomerance, Proc. Southeastern Conf. Combinatorics, Graph Theory, and Computing, Boca Raton, Florida, 1983, Cong. Num. 40 (1983), 291-304. Moduli r for which there are many small primes congruent to a modulo r, P.T. Bateman and C. Pomerance, Publ. Math. d'Orsay 83.04 (1983), 8-19. Lecture notes on primality testing and factoring - A short course at Kent State University, C. Pomerance, (based on notes by S. M. Gagola, Jr.), MAA Notes 4 (1984). New ideas for factoring large integers, C. Pomerance, J. W. Smith and S. S. Wagstaff, Jr., Advances in Cryptology, Proc. Crypto 83, D. Chaum, ed., Plenum Press, New York, 1984, 81-85. Estimates for certain sums involving the largest prime factor of an integer, A. Ivic and C. Pomerance, Proc. Colloquium on Number Theory 34 (1981), Topics in Classical Number Theory, North Holland, 1984, 769-789. On the size of the coefficients of the cyclotomic polynomial, P. T. Bateman, C. Pomerance and R. C. Vaughan, Proc. Colloquium on Number Theory 34 (1981), Topics in Classical Number Theory, North Holland, 1984, 171-202. View obstruction problems, III , T. W. Cusick and C. Pomerance, J. Number Theory 19 (1984), 131-139. The normal number of prime factors of (n), P. Erds and C. Pomerance, Rocky Mtn. J. Math. 15 (1985), 343-352. On locally repeated values of certain arithmetic functions, I, P. Erds, C. Pomerance and A. Srkzy, J. Number Theory 21 (1985), 319-332. Multiplicative relations for sums of initial k-th powers , D.E. Penney and C. Pomerance, Amer. Math. Monthly 92 (1985), 729-731. On the distribution of round numbers, C. Pomerance, Number Theory Proceedings, Ootacamund, India 1984, K. Alladi, ed., Lecture Notes in Math. 1122 (1985), 173-200. The quadratic sieve factoring algorithm , C. Pomerance, Advances in Cryptology, Proceedings of Eurocrypt 84, Paris, 1984, T. Beth. N. Cot, and I. Ingemarsson, eds., Lecture Notes in Computer Sci. 209 (1985), 169-182. On the Schnirelmann and asymptotic densities of certain sets of non-mulitples, P. Erds, C. B. Lacampagne, C. Pomerance and J. L. Selfridge, Proceedings of the Southeast Conference on Combinatorics, Graph Theory, and Computing, Boca Raton, Florida, 1985, Congressus Numerantium 48 (1985), 67-79. On sums involving reciprocals of the largest prime factor of an integer, P. Erds and A. Ivic and C. Pomerance, Glasnik Math. 21 (1986), 283-300. On the number of false witnesses for a composite number , P. Erds and C. Pomerance, Math. Comp. 46 (1986), 259-279. On primitive divisors of Mersenne numbers , C. Pomerance Acta Arith. 46 (1986), 355-367. On the distribution of the values of Euler's function, C. Pomerance, Acta Arith. 47 (1986), 63-70. On locally repeated values of certain arithmetic functions, II, P. Erds, C. Pomerance and A. Srkzy, Acta Math. Hungarica 49 (1987), 251-259. On the average number of groups of square-free order , C. Pomerance, Proc. Amer. Math. Soc. 99 (1987), 223-231. The smallest n-uniform hypergraph with positive discrepancy, N. Alon, D. J. Kleitman, C. Pomerance, M. Saks and P. Seymour, Combinatorica 7 (1987), 151-160. On locally repeated values of certain arithmetic functions, III , P. Erds, C. Pomerance and A. Srkzy, Proc. Amer. Math. Soc. 101 (1987), 1-7. Very short primality proofs , C. Pomerance, Math. Comp. 48 (1987), 315-322. Fast, rigorous factorization and discrete logarithm algorithms, C. Pomerance, Discrete algorithms and complexity, D. S. Johnson, T. Nishizeki, A. Nozaki, H. S. Wilf, eds., Academic Press, Orlando, Florida, 1987, pp. 119-143. On products of sequences of integers, C. Pomerance and A. Srkzy, Coll. Math. Soc. Janos Bolyai 51 (1987), 447-463. A pipe-line architecture for factoring large integers with the quadratic sieve algorithm, C. Pomerance, J. W. Smith and R. Tuler, SIAM J. Comput. 17 (1988), 387-403. On homogeneous multiplicative hybrid problems in number theory, C. Pomerance and A. Srkzy, Acta Arith. 49 (1988), 291-302. On the number of distinct values of Euler's -function, H. Maier and C. Pomerance, Acta Arith. 49 (1988), 263-275. On divisors of sums of integers, III , C. Pomerance, A. Srkzy and C. L. Stewart, Pacific J. Math. 133 (1988), 363-379. The generation of random numbers that are probably prime, P. Beauchemin, G. Brassard, C. Crpeau, C. Goutier and C. Pomerance, Journal of Cryptology 1 (1988), 53-64. Two methods in elementary analytic number theory, C. Pomerance, Number theory and applications, R. A. Mollin, ed., Kluwer Academic Publishers, Dordrecht, 1989, pp. 135-161. On the composition of the arithmetic functions and , C. Pomerance, Colloq. Math. 58 (1989), 11-15. The probability that a random probable prime is composite , S.H. Kim and C. Pomerance, Math. Comp. 53 (1989), 721-741. Fonction zta de Riemann et conjecture de Weyl-Berry pour les tambours fractals, M. L. Lapidus and C. Pomerance, C. R. Acad. Sci. Paris (Ser. I) 310 (1990), 343-348. On the normal behavior of the iterates of some arithmetic functions, P. Erds, A. Granville, C. Pomerance and C. Spiro, Analytic Number Theory, Proc. Conf. in honor of Paul T. Bateman, B. C. Berndt, et al. eds., Birkhauser, Boston, 1990, pp. 165-204. Unusually large gaps between consecutive primes , H. Maier and C. Pomerance, Trans. Amer. Math. Soc. 322 (1990), 201-237. On the least prime in certain arithmetic progressions, A. Granville and C. Pomerance, J. London Math. Soc. (2) 41 (1990), 193-200. Factoring, C. Pomerance, Cryptology and Computational Number Theory, C. Pomerance, ed., Proc. Symp. Appl. Math. 42, Amer. Math. Soc. Providence, 1990. Cryptology and computational number theory - an introduction, C. Pomerance, Cryptology and Computational Number Theory, C. Pomerance, ed., Proc. Symp. Appl. Math. 42, Amer. Math. Soc., Providence, 1990. On a theorem of Besicovitch: values of arithmetic functions that divide their arguments , P. Erds and C. Pomerance, Indian J. Math. 32 (1990), 279-287. On the prime divisors of Mersenne numbers , P. Erds, P. Kiss and C. Pomerance, Acta Arith. 57 (1991), 267-281. Carmichael's lambda function , P. Erds, C. Pomerance and E. Schmutz, Acta Arith. 58 (1991), 363-385. The distribution of Lucas and elliptic pseudoprimes , D.M. Gordon and C. Pomerance, Math. Comp. 57 (1991), 825-838. Grandes dviations pour certaines fonctions arithmtiques , M. Balazard, J.L. Nicolas, C. Pomerance and G. Tenenbaum, J. Number Theory 40 (1992), 146-164. The distribution of smooth numbers in arithmetic progressions , A. Balog and C. Pomerance, Proc. Amer. Math. Soc. 115 (1992), 33-43. A rigorous time bound for factoring integers , H. W. Lenstra, Jr. and C. Pomerance, J. Amer. Math. Soc. 5 (1992), 483-516. Reduction of huge, sparse matrices over a finite field via created catastrophes , C. Pomerance and J. W. Smith, Experimental Math. 1 (1992), 90-94. The Riemann zeta function and the one dimensional Weyl-Berry conjecture for fractal drums, M.L. Lapidus and C. Pomerance, Proc. London Math. Soc. (3) 66 (1993), 41-69. Average case error estimates for the strong probable prime test , I. Damgard, P. Landrock and C. Pomerance, Math. Comp. 61 (1993), 177-194. Carmichael numbers, C. Pomerance, Nieuw Arch. Wisk. 11 (1993), 199-209. On elements of sumsets with many prime factors , P. Erds, C. Pomerance, A. Srkzy and C. L. Stewart, J. Number Theory 44 (1993), 93-104. An upper bound in Goldbach's conjecture , J.M. Deshouillers, A. Granville, W. Narkiewicz and C. Pomerance, Math. Comp. 61 (1993), 209-213. Factoring integers with the number field sieve, J. Buhler, H. W. Lenstra, Jr. and C. Pomerance, The development of the number field sieve, A. K. Lenstra and H. W. Lenstra, Jr., eds., Lecture Notes in Math. 1554, pp. 50-94, Springer-Verlag, Berlin, 1993. A hyperelliptic smoothness test. I, H. W. Lenstra, Jr., J. Pila and C. Pomerance, Phil. Trans. R. Soc. London A 345 (1993), 397-408. Sixes and sevens, C. Pomerance, Missouri J. Math. Sci. 6 (1994), 62-63. There are infinitely many Carmichael numbers , W. R. Alford, A. Granville and C. Pomerance, Annals Math. 140 (1994), 703-722. On the difficulty of finding reliable witnesses, W. R. Alford, A. Granville and C. Pomerance, Algorithmic Number Theory Proceedings (ANTS-I), L. M. Adleman and M.-D. Huang, eds., Lecture Notes in Computer Sci. 877 (1994), Springer-Verlag, Berlin, pp. 1-16. Dickson polynomials with few fixed points in a finite field, C. Pomerance, J. Sichuan U. (Natural Science Ed.) 31 (1994), 460-464. On a conjecture of R. L. Graham, F. Y. Cheng and C. Pomerance, Rocky Mtn. J. Math. 24 (1994), 961-975. The number field sieve , C. Pomerance, Mathematics of Computation, 1943-1993, Fifty Years of Computational Mathematics, W. Gautschi, ed., Proc. Symp. Appl. Math. 48, American Mathematical Society, Providence, 1994, pp. 465-480. Counting the integers factorable via cyclotomic methods , C. Pomerance and J. Sorenson, J. Algorithms, 19 (1995), 250-265. On a conjecture of Crandall concerning the qx+1 problem , Z. Franco and C. Pomerance, Math. Comp. 64 (1995), 1333-1336. Implementing the self initializing quadratic sieve on a distributed network, W.R. Alford and C. Pomerance, Number Theoretic and Algebraic Methods in Computer Science, Proc. of Int'l Moscow Conference, June-July, 1993, A. J. van der Poorten, I. Shparlinski, H. G. Zimmer, eds., World Scientific, 1995, pp. 163-174. Combinatorial number theory, C. Pomerance and A. Srkzy, Handbook of Combinatorics, R. L. Graham, M. Grtschel, L. Lovsz, eds., Elsevier Science B.V., 1995, pp. 967-1018. On the role of smooth numbers in number theoretic algorithms , C. Pomerance, Proceedings of the Intenational Congress of Mathematicians, Zurich, Switzerland 1994, Birkhauser Verlag, Basel, 1995, pp. 411-422. Counterexamples to the modified Weyl-Berry conjecture, M.L. Lapidus and C. Pomerance, Math. Trans. Cambridge Phil. Soc. 119 (1996), 167-178. Symmetric and asymmetric primes , P. Fletcher, W. Lindgren and C. Pomerance, J. Number Theory 58 (1996), 89-99. Multiplicative independence for random integers, C. Pomerance, Analytic Number Theory, Proceedings of a Conference in Honor of Heini Halberstam, Vol. 2, B. Berndt, H. Diamond, A. Hildebrand, eds., Birkhauser, Boston, 1996, pp. 703-711. On the divisors of n!, P. Erds, S.W. Graham, A. Ivic and C. Pomerance, Analytic Number Theory, Proceedings of a Conference in Honor of Heini Halberstam, Vol. 1, B. Berndt, H. Diamond, A. Hildebrand, eds., Birkhauser, Boston, 1996, pp. 337-355. A tale of two sieves , C. Pomerance, The Notices of the Amer. Math. Soc. 43 (1996), 1473-1485. On primes recognizable in deterministic polynomial time, S. Konyagin and C. Pomerance, The mathematics of Paul Erds, R. L. Graham and J. Nesetril, eds., Springer-Verlag, Berlin, 1997, pp. 176-198. A search for Wieferich and Wilson primes , R. Crandall, K. Dilcher and C. Pomerance, Math. Comp. 66 (1997), 433-449. On locally repeated values of certain arithmetic functions, IV , P. Erds, C. Pomerance and A. Srkzy, The Ramanujan J. 1 (1997), 227-241. Automaticity II: Descriptional complexity in the unary case , C. Pomerance, J.M. Robson and J. Shallitt, Theoretical Computer Sci. 180 (1997), 181-201. Paul Erds, number theorist extraordinaire , C. Pomerance, The Notices of the Amer. Math. Soc. 45 (1998), 19-23. Rigorous discrete logarithm computations in finite fields via smooth polynomials , R. Lovorn Bender and C. Pomerance, AMS IP Studies in Advanced Mathematics 7 (1998), 221-232. Euler's function in residue classes , T. Dence and C. Pomerance, The Ramanujan Journal 2 (1998), 7-20. On the distribution of champs , A. Ivic and C. Pomerance, Proceedings of the Fifth Conference of the Canadian Number Theory Association, R. Gupta and K.S. Williams, eds., CRM Proc. 19 (1999), 133-139. Residue classes free of values of Euler's function, K. Ford, S. Konyagin and C. Pomerance, Number Theory in Progress, K. Gyory, H. Iwaniec, and J. Urbanowicz, eds., vol. 2, de Gruyter, Berlin and New York, 1999, pp. 805-812. On the solutions to (n) = (n+k), S.W. Graham, J.J. Holt and C. Pomerance, Number Theory in Progress, K. Gyory, H. Iwaniec, and J. Urbanowicz, eds., vol. 2, de Gruyter, Berlin and New York, 1999, pp. 867-882. Primes and factorization, J. Grantham and C. Pomerance, Handbook of Discrete Mathematics, K.H. Rosen, ed., CRC Press, 1999. Small values of the Carmichael function and cryptographic applications, J. Friedlander, C. Pomerance and I. E. Shparlinski, Proc. Workshop on Cryptography and Computational Number Theory (CCNT'99), K.-Y. Lam, I. E. Shparlinski, H. Wang, and C. Xing, eds., Birkhuser, 2001, pp. 25-32. Prime numbers: a computational perspective, R. Crandall and C. Pomerance, 545 + xvi pages, Springer-Verlag, New York, 2001. The expected number of random elements to generate a finite abelian group , C. Pomerance, Periodica Mathematica Hungarica 43 (2001), 191-198. Period of the power generator and small values of the Carmichael function , J. Friedlander, C. Pomerance and I. E. Shparlinski, Math. Comp., 70 (2001), 1591-1605. Corrigendum , op. cit., 71 (2002), 1803-1806. Two contradictory conjectures concerning Carmichael numbers , A. Granville and C. Pomerance, Math. Comp., 71 (2001), 883-908. On the problem of uniqueness for the maximal Stirling number(s) of the second kind , E.R. Canfield and C. Pomerance, Integers, 2 (2002), paper A1, 13 pp. On some problems of Makowski-Schinzel and Erds concerning the arithmetical functions and , F. Luca and C. Pomerance, Colloq. Math., 92 (2002), 111-130. Smooth orders and cryptographic applications , C. Pomerance and I.E. Shparlinski, Proc. ANTS-V, Sydney, Australia, Springer Lecture Notes in Computer Science 2369, (2002), pp. 338-348. A hyperelliptic smoothness test. II , H. W. Lenstra, Jr., J. Pila and C. Pomerance, Proc. London Math. Soc., (3) 84 (2002), 105-146. Ruth-Aaron numbers revisited , C. Pomerance, Paul Erds and his Mathematics, (Budapest, 1999), 567--579, Bolyai Soc. Math. Stud., 11, Jnos Bolyai Math. Soc., Budapest, 2002. On generalizing Artin's conjecture on primitive roots to composite moduli , S. Li and C. Pomerance, J. Reine Angew. Math. 556 (2003), 205-224. Primitive roots: a survey , S. Li and C. Pomerance, in New Aspects of Analytic Number Theory (RIMS Kokyuroku No. 1274) (Y. Tanigawa, ed.), and also in Number Theoretic Methods---Future Trends, C. Jia and S. Kanemitsu, eds., Dev. Math. 8, pp. 219-231, Kluwer Academic Publishers, Dordrecht 2002. Timed fair exchange of arbitrary signatures, J. A. Garay and C. Pomerance, in Financial Cryptography, 7th International Conference, FC 2003, Lecture Notes in Computer Science {\bf 2742}, Springer, New York, 2003, pp.~190--207. Multiplicative structure of values of the Euler function , W. D. Banks, J. B. Friedlander, C. Pomerance and I. E. Shparlinski, in High Primes and Misdemeanours: Lectures in Honour of the Sixtieth Birthday of Hugh Cowie Williams (A. Van der Poorten, ed.), Fields Inst. Comm. 41 (2004) 29-47. Heuristics for class numbers of prime-power real cyclotomic fields , J.Buhler, C. Pomerance and L.Robertson, in High Primes and Misdemeanours: Lectures in Honour of the Sixtieth Birthday of Hugh Cowie Williams (A. Van der Poorten, ed.), Fields Inst. Comm. 41 (2004), 149-157. Prime numbers and the search for extraterrestrial intelligence , C. Pomerance, in Mathematical Adventures for Students and Amateurs, D. Hayes and T. Shubin, eds., pp. 1-4, M.A.A., 2004. The largest prime factor of a Mersenne number , L. Murata and C. Pomerance, in Number Theory, CNTA Proceedings, Montreal, 2002, 209--218, CRM Proc. Lecture Notes, 36, Amer. Math. Soc., Providence, RI, 2004. On the binary expansions of algebraic numbers , D. H. Bailey, J. M. Borwein, R. E. Crandall, and C. Pomerance, J. Thorie des Nombres Bordeaux 16 (2004), 487-518. Prime Numbers: a computational perspective, second edition, R. E. Crandall and C. Pomerance, Springer, New York, 2005. On the distribution in residue classes of integers with a fixed sum of digits , C. Mauduit, C. Pomerance and A. Srkzy), Ramanujan J., special issue in honor of J.-L. Nicolas 9 (2005), 45-62. Products of ratios of consecutive integers , R. de la Bretche, C. Pomerance, and G. Tenenbaum, Ramanujan J., special issue in honor of J.-L. Nicolas 9 (2005), 131-138. The iterated Carmichael -function and the number of cycles of the power generator , G. Martin and C. Pomerance, Acta Arith. 118 (2005), 305-335. On the period of the linear congruential and power generators , P. Kurlberg and C. Pomerance, Acta Arith. 119 (2005), 149-169. Smooth numbers and the quadratic sieve , C. Pomerance, to appear in the proceedings of an MSRI workshop, J. Buhler and P. Stevenhagen, eds. Elementary thoughts on discrete logarithms , C. Pomerance, to appear in the proceedings of an MSRI workshop, J. Buhler and P. Stevenhagen, eds. Finding the group structure of elliptic curves over finite fields, J. B. Friedlander, C. Pomerance, and I. E. Shparlinski, Bull. Austral. Math. Soc., to appear. Primality testing with Gaussian periods, H. W. Lenstra, Jr. and C. Pomerance, preprint. On the average number of divisors of the Euler function, F. Luca and C. Pomerance, Publ. Math. Debrecen, to appear. Sieving by large integers and covering systems of congruences, M. Filaseta, K. Ford, S. Konyagin, C. Pomerance, and G. Yu, submitted for publication. Maximal height of divisors of x^n-1, C. Pomerance and N. C. Ryan, submitted for publication. Irreducible radical extensions and Euler-function chains F. Luca and C. Pomerance, preprint. Last modified on October 29, 2005 by the owner.
Pollack, David
Wesleyan University. Thesis "Explicit Hecke Actions on Modular Forms", Harvard, 1998 (PDF).
David Pollack Faculty, Staff, and Graduate Students Undergrad Math Program Calendar of Events Graduate Program Undergrad CS Program Contact Us People Faculty Staff Graduate Students David Pollack Email dpollack--wesleyan.edu Homepage Back to Faculty Staff Listing http: www.math-cs.wesleyan.edu 265 Church Street Middletown, CT 06459 (860) 685-2620 jgibb@wesleyan.edu
Pizer, Arnold
University of Rochester. Arithmetic of quaternion algebras and its connections to modular forms, Brandt matrices, Hecke operators, and Ramanujan graphs. Pedagogical use of the internet.
UR Department of Mathematics - Arnold Pizer Arnold Pizer, Professor, Associate Chair Department of Mathematics University of Rochester Rochester, NY 14627 Office: Hylan 802 Phone: (716) 275-7767 Fax: (716) 273-4655 E-mail: apizer@math.rochester.edu Biographical Sketch Prof. Pizer received his B.A. in Mathematics (1967) from Yale University, and his Ph.D. in Mathematics (1971), also from Yale. His thesis advisor was T. Tamagawa. He was an Acting Assistant Professor at UCLA (1971-73) and an Assistant Professor at Brandeis (1973-76) before joining the University as an Assistant Professor of Mathematics in 1976. He was promoted to Associate Professor in 1978 and to Professor in 1989. He currently is Associate Chair of the Department of Mathematics. Research Prof. Pizer's research interests are in the field of Number Theory. Prof. Pizer is particularly interested in the study of the arithmetic of quaternion algebras and its connections to modular forms, Brandt matrices, Hecke operators, and Ramanujan graphs. Much of his work has been related to the "Basis Problem" which involves constructing explicit bases for spaces modular forms from theta series attached to quaternion algebras and determining the action of Hecke operators on such bases. Currently he is interested in developing a "ray class" ideal theory for orders in quaternion algebras in analogy with ray class" theory in number fields and the application of such a theory to Ramanujan graphs. Prof. Pizer is also has a pedagogical interest in using the internet for mathematics education. He is a codeveloper, together with Prof. Gage, of the homework delivery system WeBWorK. WeBWorK Outline of MAA Minicourse on WeBWorK San Diego, January, 2002 Photos Personal Photos
Petsche, Clayton
University of Georgia. Diophantine geometry and arithmetic; Local and global heights on algebraic varieties; Uniform distribution on locally compact groups; Applications of harmonic analysis to number theory; Mahler measure of polynomials. Teaching notes.
Clayton Petsche Clayton Petsche VIGRE Postdoctoral Associate Department of Mathematics The University of Georgia Contact Information. Office. Boyd Graduate Research Center, Room 526. Office Hours. Tues. 11-12, Wed. 1-3:30, and by appointment. Mailing Address. Department of Mathematics; The University of Georgia; Athens, GA 30602-7403; U.S.A. Email. clayton at math.uga.edu Papers. Global discrepancy and small points on elliptic curves. (with Matthew Baker). Submitted for publication. ( preprint available in pdf ) Small rational points on elliptic curves over number fields. Submitted for publication. ( preprint available in pdf ) A quantitative version of Bilu's equidistribution theorem. International Journal of Number Theory, Vol. 1, No. 2 (2005) 281-291. ( preprint available in pdf ) The distribution of Galois orbits of low height. Ph.D. Dissertation, The University of Texas at Austin, 2003. Courses. Fall 2005. Modern Algebra and Geometry I. Spring 2005. Introduction to Higher Mathematics. Fall 2004. Analytic Geometry and Calculus. Job Application Materials. Curriculum Vitae. (coming soon...) Research Statement. (coming soon...) Teaching Statement. (coming soon...) The content and opinions expressed on this Web page do not necessarily reflect the views of nor are they endorsed by the University of Georgia or the University System of Georgia.
Pacelli, Allison M.
Williams College. Arithmetic of function fields. Preprints, teaching information.
Allison M. Pacelli, Williams College Allison M. Pacelli Williams College Department of Mathematics and Statistics Bronfman Science Center Williams College Williamstown, MA 01267 apacelli@williams.edu 413-597-4708 Bronfman Science Center, Room 200 Education: BROWN UNIVERSITY Providence, RI, Ph.D., Mathematics, May 2003. Advisor: Michael Rosen Dissertation Title: The Structure of the Class Group in Global Function Fields UNION COLLEGE Schenectady, New York, B.S., Mathematics, June 1997. Summa Cum Laude, Departmental Honors Phi Beta Kappa, 1996 Further Information Curriculum Vitae Publications Courses: Spring 2005: Math 180, The Art of Mathematical Thinking: An Introduction to the Beauty and Power of Mathematical Ideas (Course website on Blackboard) Math 414, Galois Theory (Course website on Blackboard) Fall 2004: Math 175, Mathematical Politics: Voting, Power, and Conflict (Course website on Blackboard) Math 211, Linear Algebra (Course website on Blackboard) Spring 2004: Math 211, Linear Algebra (Course website on Blackboard) Math 314, Polynomial Arithmetic (Course website on Blackboard) Fall 2003: Math 211, Linear Algebra (Course website on Blackboard) Courses Taught at Brown University: Linear Algebra Number Theory and the Art of Mathematical Proof Introduction to Calculus I Introduction to Calculus II Analytic Geometry and Calculus Advanced Placement Calculus Links: WILLIAMS RELATED MATHEMATICS LINKS FOR UNDERGRADUATES Math Department Mathematical Association of American Careers in Math Blackboard American Mathematical Society Career Profiles in Math Association for Women in Mathematics Hudson River Undergraduate Math Conference Summer Research Opportunities Budapest Semester in Mathematics Math Horizons - MAA Student Magazine E-mail me
Prasanna, Kartik
UCLA. Modular forms. Thesis, teaching information.
index Kartik Prasanna Hedrick Assistant Professor Department of Mathematics, University of California, Los Angeles, CA 90095. Office Phone: (310) 794 6646 e-mail address: kartikp@math.ucla.edu LINKS NUMBER THEORY SEMINAR CV Research Personal COURSES MATH 115AH SPRING 2005 MATH 2 WINTER 2005 MATH 110B WINTER 2005 MATH 110A FALL 2004 MATH 33A SPRING 2004 MATH 110A FALL 2003 MATH 132 FALL 2003 MATH 111 WINTER 2004 E-mail me UCLA Homepage UCLA Math Dept.
Papanikolas, Matt
Texas A+M University. Number theory and arithmetic geometry: elliptic curves and Drinfeld modules, in particular canonical heights, special values of analytic functions, L-series and modular forms.
Matt Papanikolas Matt Papanikolas Assistant Professor Department of Mathematics Texas AM University College Station, TX 77843-3368 Office: Milner 321 Phone: Dept: Fax: (979) 845-1615 (979) 845-7554 (979) 845-6028 Email: map@math.tamu.edu Schedule Fall 2005 Teaching: Math 662: Algebraic Number Theory , MWF 1:50-2:40 Office Hours: Mon. Fri. 11-12 Texas AM Number Theory Group Texas AM Number Theory Seminar Wednesdays, 12:30-1:30, Milner 317 ArithmeTexas, April 2-3, 2005 Education Ph.D. in Mathematics , Brown University , 1998. A.B. in Mathematics , Amherst College , 1992. Research Interests Number theory and arithmetic geometry. I'm interested in elliptic curves and Drinfeld modules, and in particular I work on canonical heights, special values of analytic functions, L-series and modular forms. Curriculum Vitae My research is currently sponsored by a grant from the National Science Foundation . Teaching Information Selected Publications and Preprints ( Complete List ) On the torsion of Jacobians of principal modular curves of level 3^n (with C. Rasmussen) submitted for publication, 8 pages. [ PDF ] Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms , submitted for publication, 53 pages. [ PDF | Arxiv.org ] A formula and a congruence for Ramanujan's tau-function Proceedings of the American Mathematical Society, accepted for publication, 9 pages. [ PDF ] Extensions of abelian varieties defined over a number field (with N. Ramachandran) Journal of Number Theory 112 (2005), 386-400. [ Journal | Arxiv.org ] Combinatorics of traces of Hecke operators (with S. Frechette and K. Ono) Proceedings of the National Academy of Sciences, USA, 101 (2004), 17016-17020. [ Journal ] Gaussian hypergeometric functions and traces of Hecke operators (with S. Frechette and K. Ono) International Mathematics Research Notices, 2004, no. 60, 3233-3262. [ Journal ] Determination of the algebraic relations among special Gamma-values in positive characteristic (with G. W. Anderson and W. D. Brownawell) Annals of Mathematics 160 (2004), 237-313. [ Journal | Arxiv.org ] Higher Weierstrass points on X_0(p) (with S. Ahlgren) Transactions of the American Mathematical Society 355 (2003), 1521-1535. [ Journal ] A Weil-Barsotti formula for Drinfeld modules (with N. Ramachandran) Journal of Number Theory 98 (2003), 407-431. [ Journal | Arxiv.org ] Linear independence of Gamma values in positive characteristic (with W. D. Brownawell) Journal fr die reine und angewandte Mathematik 549 (2002), 91-148. [ Journal | Arxiv.org ] Canonical heights on elliptic curves in characteristic p Compositio Mathematica 122 (2000), 299-313. [ Journal | Arxiv.org ] Upcoming Schedule Arithmetic Geometry of Higher Dimensional Varieties, Fields Institute, Toronto, November 5-6, 2005 Joint Meeting of the American Mathematical Society and the Taiwanese Mathematical Society , Taichung, December 14-18, 2005 American Mathematical Society Joint Meetings , Special Session on Arithmetic Geometry and Modular Forms, San Antonio, January 12-15, 2006 Ninth Meeting of the Canadian Number Theory Association, Vancouver, July 2006 Personal Information I grew up in Tucson, Arizona . My wife is a painter - you can view some of her work here . Interesting Places Mathematical Number Theory at Texas AM American Mathematical Society arXiv.org Math e-Print Archive Number Theory Web Lots of math links General Hera Gallery U.S. Masters Swimming Linux Online College Station Weather Last modified on September 30, 2005
Peneva, Temenoujka
University of Plovdiv "Paisii Hilendarski". Analytic number theory: additive prime number theory, distribution of primes, exponential sums, sieve methods, Riemann zeta-function and Dirichlet L-functions.
Home Page of Temenoujka Peneva Home Page of Temenoujka Peneva Research Interests Publications Professional Information Contact Information Links Assistant Professor, Ph.D. University of Plovdiv "Paisii Hilendarski" Faculty of Mathematics and Informatics Department of Complex Analysis and Differential Equations 236 Bulgaria Blvd., 4003 Plovdiv, Bulgaria Office: (+359) 32 277 278, Cell: (+359) 88 857 432 E-mail: tpeneva@pu.acad.bg _______________________________ Research Interests Analytic number theory, with particular interest in additive prime number theory, the distribution of primes, exponential sums, sieve methods, Riemann zeta-function and Dirichlet L-functions. Back to the top of this page ___________________________ Publications Refereed Journals An Additive Problem with Piatetski-Shapiro Primes and Almost-Primes, [ps] , to appear in Monatshefte fr Mathematik. Corrigendum: "On the Exceptional Set for Goldbach's Problem in Short Intervals", [ps] , submitted to Monatshefte fr Mathematik. On the Exceptional Set for Goldbach's Problem in Short Intervals, Monatshefte fr Mathematik 132 (2001), 49-65. On the Ternary Goldbach Problem with Primes pi such that pi+2 are Almost-Primes, Acta Mathematica Hungarica 86 (4) (2000), 305-318. An Additive Problem with Primes and Almost-Primes (with D. I. Tolev), Acta Arithmetica 83 (2) (1998), 155-169. Conference Proceedings An Additive Problem with Piatetski-Shapiro Primes and Almost-Primes, in Proceedings of the Symposium on New Aspects of Analytic Number Theory (Kyoto, 2001), Surikaisekikenkyusho Kokyuroku 1274 (2002), 193-201. On the Exceptional Set in Goldbach's Problem, in Proceedings of the Symposium on Analytic Number Theory and Related Topics (Kyoto, 1999), Surikaisekikenkyusho Kokyuroku 1160 (2000), 32-39. On Some Additive Problems with Primes and Almost-Primes, in Proceedings of the Symposium on Analytic Number Theory and its Interactions with Other Parts of Number Theory (Kyoto, 1998), Surikaisekikenkyusho Kokyuroku 1091 (1999), 233-240. Work in Progress On sums of primes and k-th powers (with J. Brdern). On the Piatetski-Shapiro Prime-Almost-Prime Twins. Problems in Complex Analysis (textbook, with I. Kasandrova) Back to the top of this page _______________________________ Professional Information Education Ph.D. in Mathematics, University of Tsukuba, Japan, March 2002. Thesis title: On some additive problems in analytic number theory. Advisor: Dr. Hiroshi Mikawa. B.A. and M.S. in Mathematics, University of Plovdiv, Bulgaria, July 1995. Thesis title: Applications of the zero-density estimates for the zeta-function of Riemann in number theory. Advisor: Assoc. Prof. Dr. Doychin Tolev. Research Fellowships University of Stuttgart, Germany, Scholarship of the German Academic Exchange Service (DAAD), September - October 2002. University of Tsukuba, Japan, Scholarship of the Japanese Ministry of Education, Science and Culture, April 1998 - March 2002. University College, London, and Magdalen College, Oxford, UK, Sponsored by Tempus-Phare Joint European Project S_JEP-11087-96, October - December 1997. Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary, Scholarship of the Bulgarian Ministry of Science and Education, October 1996. University of Plovdiv, Bulgaria, Scholarship of the Bulgarian Ministry of Science and Education, January 1996 - March 1998. Academic Awards Distinguished award of the Hardy-Ramanujan Society, [pdf] , for the result in: On the Exceptional Set for Goldbach's Problem in Short Intervals, Monatshefte fr Mathematik 132 (2001), 49-65. Award of the National Academic Foundation, Bulgaria, for excellent academic performance, May 1994. Teaching Experience Taught the following subjects at the University of Plovdiv, Bulgaria: Complex Analysis Functional Analysis Ordinary Differential Equations Conference and Seminar Presentations On Some Additive Problems with Primes in Analytic Number Theory, Invited Talk for the Algebra Seminar at the Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, Bulgaria, November 2002. On an Additive Problem with Piatetski-Shapiro Primes, Invited Talk for the Number Theory Seminar at the University of Stuttgart, Germany, October 2002. On an Additive Problem with Piatetski-Shapiro Primes and Almost-Primes, Invited Talk for Analytic Number Theory Seminar at Meiji-Gakuin University, Tokyo, Japan, December 2001. On an Additive Problem with Piatetski-Shapiro Primes and Almost-Primes, Invited Lecture for the Symposium on New Aspects of Analytic Number Theory, Research Institute for Mathematical Science, Kyoto, Japan, November 2001. On the Exceptional Set for Goldbach's Problem in Short Intervals, Millennial Conference on Number Theory, University of Illinois, Urbana-Champaign, USA, May 2000. On the Exceptional Set in Goldbach's Problem, Invited Lecture for the Symposium on Analytic Number Theory and Related Topics, Research Institute for Mathematical Science, Kyoto, Japan, November 1999. On Some Additive Problems with Primes and Almost-Primes, Invited Lecture for the Symposium on Analytic Number Theory and its Interactions with Other Parts of Number Theory, Research Institute for Mathematical Science, Kyoto, Japan, October 1998. On Some Additive Problems with Primes and Almost-Primes, Invited Talk for the Analytic Number Theory Seminar at Meiji-Gakuin University, Tokyo, Japan, July 1998. Conferences and Seminars Attended Winter School on Partial Differential Equations with Singularities, University of Novi Sad, Novi Sad, Serbia and Montenegro, February 2003. Workshop on Financial Mathematics, University of Plovdiv, Plovdiv, Bulgaria, December 2002. Analytic Number Theory Seminar (held once every three weeks), Meiji-Gakuin University, Tokyo, Japan, April 1998 - March 2002. Symposium on New Aspects of Analytic Number Theory, Research Institute for Mathematical Science, Kyoto, Japan, November 2001. Millennial Conference on Number Theory, University of Illinois, Urbana-Champaign, USA, May 2000 ( participants' photo ). Symposium on Analytic Number Theory and Related Topics, Research Institute for Mathematical Science, Kyoto, Japan, November 1999. Symposium on Analytic Number Theory and its Interactions with Other Parts of Number Theory, Research Institute for Mathematical Science, Kyoto, Japan, October 1998. Meeting in Honor of G. H. Hardy's Anniversary, Mathematical Institute, University of Oxford, Oxford, UK, December 1997. Zeta Functions and Spectra, London Mathematical Society Spitalfields Meeting, Isaac Newton Institute, Cambridge, UK, November 1997. Arithmetic Seminars (held once weekly), Mathematical Institute, University of Oxford, UK, October - December 1997. Back to the top of this page _______________________________ LInks Faculty of Mathematics and Informatics, University of Plovdiv Institute of Mathematics and Informatics, University of Tsukuba Number Theory Web American Mathematical Society Analytic Number Theory in Japan Back to the top of this page options Last modified on March 30, 2003. geovisit();
Pollard, John M.
Factoring, discrete logarithms. Originator of the p-1, lambda, rho and kangaroo methods.
JOHN M POLLARD`S HOME PAGE Easterwas 27th March, 2005. Music(including some local events) Number Theory, other mathematics and puzzles Tidmarsh and Sulham(villages in Berkshire, UK) and surrounding area There are many John Pollard`s to be found on the web, but fewer with my middle initial M. This onelives in the village of Tidmarsh (near Reading, Berks, UK). The pages listed above are probably of interest to different groups of people. They are mainly collections of links. Comments about these pages are welcome. Apologies for the advertisments, added recently by Lycos, without my agreement! (Those obscuring text do soon go away). New Email: jmp at tidcott dot fsnet dot co dot uk URL: members.lycos.co.uk John_M_Pollard Last modified:12 April2005
Odgers, Ben
University of Bristol. Prime numbers, the Riemann zeta function, L-functions, and random matrix theory.
The Homepage of Ben Odgers Home My Mathematics Page Bristol Mathematics Home Position: I'm a PhD student in Mathematics under the supervision of Prof. Jon Keating . My research interests are broadly described by the link between Number Theory and Random Matrix Theory. Contact details: School of Mathematics, University of Bristol, University Walk, Clifton, Bristol. BS8 1TW Mobile: +44 7969 54 7282 email: ben.odgers@bristol.ac.uk
Oman, Karl
Thiel College. Elementary and Algebraic Number Theory: Powerful Numbers, the abc Conjecture, and Ramanujan-Nagell Equations. Teaching information, Problem of the Week.
Dr. Karl K. Oman Dept of Math Comp Sci Problem of the Week Course Offerings Major Minor Requirements Experiential Learning Faculty Kappa Mu Epsilon Past Commendations Resources Useful Links Actuarial Studies Major Requirements Office: AC-135 Phone: 724-589-2033 Fax: 724-589-2021 e-mail: koman@thiel.edu Back to Department of Mathematics and Computer Science Academics Current Students Athletics Faculty Staff Alumni About Thiel College Prospective Students News Events Special Programs Visitors
Oyono, Roger
Universitt Duisburg-Essen. Arithmetic on Jacobians. Publications, thesis.
Roger Oyono's Homepage Roger Oyono Institut fr Experimentelle Mathematik (IEM) Arbeitsgruppe Zahlentheorie Universitt Duisburg-Essen Ellernstrae 29 D-45326 Essen Room 304 Tel.: +49 (0) 201-183-7682 e-mail: oyono@exp-math.uni-essen.de Thesis and Publications Buekenhout-Metz-Unitale in PG(2, q^2), Diplom-thesis, Mathematisches Institut Giessen, Mai 2000 ( dvi , ps , pdf ) Fast arithmetic on Jacobians of Picard curves (with S. Flon ) PKC 2004 , LNCS 2947, pp. 55-68, 2004 On Using Expansions to the Base of -2 (with R. Avanzi, T. Lange and G. Frey) To appear in Int. J. of. Comp. Math., 2004 Preprint Fast addition on non-hyperelliptic genus 3 curves, (with S. Flon and C. Ritzenthaler ) Conferences Workshop "Mathematics of Discrete Logarithms", Essen, Oct. 2003 HGI-Seminar Kryptographie Datensicherheit, Bochum, Feb. 2004 2004 International Workshop on Practice and Theory in Public Key Cryptography, Singapore, Mar. 2004 Seminaire de Theorie des Nombres de Tunis, Mar. 2004 Programs Fast arithmetic on the Jacobian of non-hyperelliptic curves of genus 3. Links I'm a member of the Graduate School on "Cryptography" (supported by the DFG ) Cryptool Some friends S. Flon , S. Omar , G. Blady Last update March 29, 2004 Kostenlose Zhler
Ochiai, Tadashi
Osaka University. Number theory, arithmetic geometry. Papers, preprints.
Tadashi Ochiai's Home Page Tadashi Ochiai's Home Page Japanese version is here. Selfintroduction NameTadashi Ochiai Status: Lecturer at Graduate school of Science, Osaka University Major Number theory or Arithmetic geometry My work email: ochiai@math.wani.osaka-u.ac.jp
Ouyang, Yi
University of Toronto. Algebraic number theory and arithmetic geometry: cohomological tools to study the arithmetic properties of number fields. Publications.
Yi Ouyang's Homepage Yi Ouyang, Postdoctoral Fellow Department of Mathematics University of Toronto 100 St. George Street Toronto, ON M5S 3G3, Canada Phone: (416) 978-4156, (905) 828-3841 Fax: (416) 978-4107 Email: youyang@math.toronto.edu Office: Sidney Smith 5016F or South Building 3023C(UTM) Welcome to my homepage. I hope you enjoy your stay here. My name is Yi Ouyang and in Chinese Ou Yang Yi. I am a postdoctoral fellow of the Department of Mathematics at the University of Toronto. Education I got both my BS and MS degrees from the Department of Mathematics at the University of Science and Technology of China , the youngest of the most prestigious universities in China and the proudest of all. You can find some information about my undergraduate study from our class homepage Class 8901 . In 1995, I spent a year at Department of Mathematics of the Ohio State University . My four years study(1996-2000) at Department of Mathematics of the University of Minnesota ended up with my Ph.D degree in June 2000 under the instruction of Professor Greg William Anderson . Research My specialty is algebraic number theory and arithmetic geometry. More specifically, I apply cohomological tools to study the arithmetic properties of number fields. One topic I am studying is the universal norm distributions, which appears quite often in the theory of cyclotomic fields, elliptic curves and modular curves. I determined the group cohomology of some universal norm distributions and used the results to study the Kolyvagin recursions in Euler systems. The other topic I am studying is about the Mordell-Weil group and Selmer group of an abelian variety in number fields, in particular, in a tower of unramified extensions. I am also participating activities in the GANITA lab. I am interested in the theoretical part of cryptography based on abelian varieties. You may find more information about my work here: AMS Coversheet ( .dvi and .pdf ) Curriculum Vitae ( .dvi and .pdf ). Past Research ( .dvi and .pdf ). Current Research interest ( .dvi and .pdf ) Publications: Riemann-Hurwitz formula in basic $Z_S$-extension (with Fei Xu), Acta Arith. 81.1(1997), 1-10. The group cohomology of universal ordinary distribution and its applications, Thesis, University of Minnesota, 2000 ( .dvi and .pdf ). The group cohomology of universal ordinary distribution, J. reine. angew. Math. 537(2001), 1--32. The universal norm distribution and Sinnott's index formula, Proceedings of AMS Vol. 130(2002), No.8 , 2203-2213. A note on the cyclotomic Euler systems and the double complex method (with Greg Anderson), to appear, Canadian Journal of Mathematics ( .dvi and .pdf ). On the universal norm distribution, submitted, 2002 ( .dvi and .pdf ). The universal Kolyvagin recursion implies the Kolyvagin recursion, submitted, 2002 ( .dvi and .pdf ). Other Math Links My thesis advisor Professor Greg W. Anderson . Professor Kumar Murty and the GANITA lab . IHES , a great place I visited in January-June 2001. Number theory on the web . Algebraic Number Theory Archives . e-Math and MathSciNet . arXiv.org e-Print archive-Mathematics . Mathematics Information Servers (Cool stuff in Math!). Teaching in Erindale College MAT498 : Topics in Mathematics, Spring 2002. MAT448: Algebra, Fall 2002. Other information: Some non-mathematical Links I visit frequently. A poem for the (good. sad?) old days.
Osburn, Robert
McMaster University. Modular forms, combinatorics, partition function. Publications.
Homepage Robert Osburn Postdoctoral Fellow Mathematics Statistics Department McMaster University Hamilton, Ontario, Canada (905) 525-9140 Ext. 23320 osburnr@icarus.math.mcmaster.ca CV: dvi pdf ps or html Research Research Statement: dvi pdf ps Teaching: Math 4E03 701 Stat 1L03E Teaching Statement: dvi pdf ps Algebra Number Theory Seminar Personal
Okazaki, Ryotaro
Doshisha University. Unit Equation; Class Field Theory of CM-fields; Continued Fractions. Papers, teaching materials.
Home Page of Ryotaro Okazaki Home Page of Ryotaro Okazaki Doshisha University Department of Knowledge Engineering and Computer Sciences, 1-3 Tataramiyakodani, Kyotanabe-shi, Kyoto-fu, 610-0394 Japan, tel: +81-774-65-6653 (dial-in) fax: +81-774-65-6801 email: rokazaki@mail.doshisha.ac.jp office: room SC523 Click here for Japanese Research I study three subjects in the theory of numbers. They are Unit Equation, Class Field Theory of CM-fields and Continued Fractions. The first two are related with algebraic cryptography. The last one is a tool for the first two but is interesting by itself. Click here for the list of papers. Click here for a list of conferences. Click here for related links. Teaching I teach basics of mathematics. This year I have 3 courses: Calculus I (Spring Term) , Mathematics for Computer Sciences I (Autumn Term) , Mathematics for Computer Sciences II (Spring Term) . I will talk on the role of the latter two courses in the lecture of July 02 in the course Perspectives on Knowledge Engineering and Computer Sciences I. I also guide Basics of Peripheral Interface Controller in Laboratory for Knowledge Engineering and Computer Sciences I and Synthesis of Compiler in Laboratory for Knowledge Engineering and Computer Sciences III. History of this Home Page 2002 Opening of this home page 2002 Calculus I 2003 Calculus I 2003 Mathematics for Computer Sciences II
Ohno, Yasuo
Kinki University. Siegel modular forms and Jacobi forms; Zeta functions associated with prehomogeneous vector spaces; Poly-Bernoulli numbers; Invariant theory. Papers, theses.
ohno Japanese version is here . Yasuo Ohno ( Number Theory ) R E S E A R C H P A P E R S (single) A conjecture on coincidence among the zeta functions associated with the space of binary cubic forms, Amer. J. Math. 119 (1997), 1083-1094. (single) A generalization of the duality and sum formulas on the multiple zeta values, J. Number Theory 74 (1999), 39-43. (single) On multiple harmonic series, preprint (1998). (single) A proof of the cyclic sum conjecture for multiple zeta values, preprint (Max-Planck-Institut PREPRINT SERIES 2000). with Don Zagier Multiple zeta values of fixed weight, depth, adn height, preprint (2000) to appear in Indag. Math. with Michael Hoffman Relations of multiple zeta values and their algebraic expression, preprint(2000). with Gunther Cornelissen "On certain multiple zeta series", (in preparation). P R O C E E D I N G S (single) Zeta functions of binary cubic forms, History and Prospect, Kyotodaigaku Surikaisekikenkyusho Koukyuroku 924 (1995), 134-152. (single) Relations among multiple zeta values, Proc. of 5th Summer School on Number Theory (1997), 197-204. (single) Multiple zeta values and a zeta function related to poly-Bernoulli numbers, Proc. of 3rd. Sympos. on Number Theory at Tsudajyuku Univ., (1998), 98-107. (single) Certain family of relations among multiple zeta values, Proc. of 15th Sympos. on Alg. Combin. Theory, (1998), 222-231. (single) Multiple zeta values and Arakawa-Kaneko's zeta function, Waseda Univ. Proc. of Sympos. on Number Theory, vol.X, (1999), 57-66. (single) Special values of multiple zeta function and Arakawa-Kaneko's zeta function, Proc. of 16th Sympos. on Alg. Combin. Theory, (1999), 38-46. T H E S E S Master Thesis Study of the zeta functions associated with the space of binary cubic forms, Osaka Univ. (1995). Doctoral Thesis A generalization of the duality and the sum formula on the multiple zeta values, Osaka Univ. (1998). I N T E R E S T S Current Research Q-linear relations among multiple zeta values Integral binary cubic forms, Zeta functions associated with certain regular irreducible prehomogeneous vector spaces. Research Interests Siegel modular forms and Jacobi forms, Zeta functions associated with prehomogeneous vector spaces, Poly-Bernoulli numbers, Invariant theory. Y A S U O . O H N O ohno@math.kindai.ac.jp
Oort, Frans
University of Utrecht. Algebraic geometry and number theory. Publications, links.
Homepage for Frans Oort Department of Mathematics Frans Oort Department of Mathematics University of Utrecht P.O.Box 80.010 3508 TA Utrecht The Netherlands tel: +31-30-2531514 ... 1425 ... 1430 ... 1420 fax: +31-30-2518394 email address email: oort at math dot uu dot nl Mathematical Institute Budapestlaan 6 3584 CD Utrecht ps file of "List of publications of Frans Oort". ps file of "Some questions in algebraic geometry". ps file of "Open problems in algebraic geometry". ps file of "Newton polygons and p-divisible groups: a conjecture by Grothendieck". ps file of "A stratification of a moduli space of abelian varieties". ps file of "Newton Polygon strata in the moduli space of abelian varieties". ps file of "Anabelian number theory and geometry. Workshop, Lorentz Center Leiden, 3-4-5 XII 2001". ps file of "An aspect of harmony in music of Johann Sebastian Bach". pdf file of "An aspect of harmony in music of Johann Sebastian Bach". A. J. de Jong \ F. Oort " Purity of the stratification by Newton polygons". ps file of A. J. de Jong \ F. Oort: Seminar on Algebraic Geometry, MIT 2002. ps file of F. Oort \ T. Zink: Families of p-divisible groups with constant Newton polygon. ps file of F. Oort: Foliations in moduli spaces of abelian varieties. ps file of S. J. Edixhoven, B. J. J. Moonen \ F. Oort (Editors) -- Open problems in algebraic geometry. Bull. Sci. Math. {\bf 125} (2001), 1 - 22. ps file of F. Oort: Minimal p-divisible groups. ps file of F. Oort: Stratifications and foliations of moduli spaces, Seminar Yuri Manin, Bonn, 30 - VII - 2002. ps file of F. Oort: Purity reconsidered. ps file of F. Oort: Monodromy, Hecke orbits and Newton polygon strata, talk Bonn 24 - II - 2003. ps file of F. Oort: Abelian varieties over finite fields, talk Berkeley 22 - III - 2003. ps file of F. Oort: Lifting an automorphism of a curve to characteristic zero, talk at the University of Pennsylvania, 7 - V - 2003. ps file of F. Oort: Hecke orbits and stratifications in moduli spaces of abelian varieties , talk at the Orsay SAGA, 14 - X - 2003. ps file of F. Oort: Special points in Shimura varieties, an introduction, talk at the IC Seminar, 14 - XI - 2003. ps file of Ching-Li Chai F. Oort: Hypersymmetric abelian varieties. ps file of F. Oort: Hecke orbits in moduli spaces of abelian varieties and foliations. Manuscript 12 pp. Number theory day, Zrich, 2 - IV - 2004. ps file of F. Oort: Abelian varieites isogous to a Jacobian. Manuscript 8 pp. Workshop Automorphisms of Curves, Leiden August 2004. ps file of F. Oort: Simple finite group schemes. New title: Simple p-kernels of p-divisible groups Manuscript 29 pp. June 2004, revised January 2005. To be published in Advances in Mathematics. ps file of F. Oort: Abelian varieties and p-divisible groups. February 2005. Manuscript 10 pp. Yuri Manin's Emeritierung Conference. ps file of F. Oort: Abelian varieties over finite fields. March 2005. Manuscript 26 pp. Gael: Luminy 21 - 25 March 2005. ps file of F. Oort: Foliations in moduli spaces of abelian varieties and dimension of leaves. Felix-Klein-Kolloquium, Dsseldorf 2 - VII - 2005. Manuscript 21 pp. 2005. ps file of F. Oort: Hecke orbits in moduli spaces. Seattle: 2005 AMS Summer Institute on Algebraic Geometry. Sheets, 22 pp. August 2005. ps file of F. Oort: Stratifications and foliations of moduli spaces of abelian varieties. 27 pp. November 2005. Algebraic Geometry and Beyond: Kyoto December 2005. Here are some links to other people in Algebraic Geometry and or Number Theory: Ahmed Abbes Universit de Paris 13 Dan Abramovich at Boston University Francesco Baldassarri at Padua University Pierre Berthelot at the University of Rennes 1 Frits Beukers at the University of Utrecht Ching-Li Chai at the University of Pennsylvania, Philadelphia PA, USA Robert Coleman at the University of California, Berkeley Brian Conrad at the University of Michigan Gunther Cornelissen at the University of Utrecht Jan Denef at the University of Leuven Christopher Deninger at the University of Mnster Bas Edixhoven at the University Leiden. Gerard van der Geer at the University of Amsterdam Eyal Goren at McGill Shushi Harashita at Hokkaido University Johan de Jong at M.I.T. Johan de Jong at Columbia University, New York. Fumiharu Kato at Kyoto University. Nicholas M. Katz at Princeton University. Kiran Sridhara Kedlaya at M.I.T. Minhyong Kim at the University of Arizona Hanspeter Kraft at Basel University. Hendrik Lenstra at the University of Leiden. Ronald van Luijk at the University of California, Berkeley. Dino Lorenzini at the University of Georgia Michel Matignon at Bordeaux. Barry Mazur at Harvard university. Ben Moonen at the University of Amsterdam Rutger Noot at the Universit Louis Pasteur, Strasbourg Arthur Ogus at the University of California, Berkeley Richard Pink at the ETH, Zrich Richard Pink, Publications and Preprints at the ETH, Zrich Bjorn Poonen at the University of California, Berkeley Ken Ribet at the University of California, Berkeley Rene' Schoof in Rome Joe Silverman at Brown University Bart de Smit at the University of Leiden Richard Taylor at Harvard University Jaap Top at the University of Groningen Emmanuel Ullmo Univ. Paris Sud Orsay Torsten Wedhorn at Bonn University Chia-Fu Yu at Columbia University Noriko Yui at Queen's University Hui June Zhu at McMaster Thomas Zink at the University of Bielefeld Number Theory Web (Australian site) Geometry Net Number Theorists' Home Pages Departmental Listings MathSciNet Last update: 16 - XI - 2005
Ono, Ken
University of Wisconsin. Combinatorics and Number Theory involving Elliptic curves, L-functions, modular forms and partitions. Publications, activities, resources.
Ken Ono's Home Page Ken Ono Solle P. and Margaret Manasse Professor of Letters and Science Department of Mathematics Van Vleck Hall University of Wisconsin Madison, Wisconsin 53706 Phone: (608) 263-2604 Email: ono(at)math(dot)wisc(dot)edu Spring 2006 Teaching: Math 567, Number Theory, MWF 8:50-9:40 am, Van Vleck B321. The web of modularity, CBMS Monograph, 2004. UW Madison VIGRE Program. 2006 REU in Number Theory. 2005 REU in Number Theory. 2003 REU in Number Theory. Aspen Skating in 2004. Aspen Skating in 2005. Windsurfing in Montana. Silly action photos: 1 2 3 A Very old picture. (Can you find me?) Number Theory Seminar. UW Algebra, Combinatorics and Number Theory Group. Publications Research Interests Combinatorics and Number Theory involving Elliptic curves, L-functions, modular forms and partitions. Editorial Boards. Integers. The International Mathematical Journal. The International Journal of Number Theory . The Ramanujan Journal. Proceedings of the American Mathematical Society. Former Graduate Students Lawrence Sze, PhD 1998, Penn State University Present Position: Tenured professor at Cal Poly, San Luis Obispo. Maki Murata, M.A. Winter 1999, Penn State University. First job: Research Scientist, Panasonic, Tokyo, Japan. Jeremy Lovejoy, PhD Summer 2000, Penn State University (Co-advisor: G. Andrews). First Job: Van Vleck Assistant Professor, University of Wisconsin. Present Position: CNRS Researcher, Universite Paris (Jussieu). Matthew Boylan, PhD Summer 2002, University of Wisconsin. First Job: NSF VIGRE Postdoctoral Fellowship, University of Illinois at Urbana-Champaign. Present Position: Palmetto Professor of Mathematics (endowed tenure track position), University of South Carolina. Emre Alkan, PhD Spring 2003, University of Wisconsin. First Job: J. L. Doob Research Assistant Professor, University of Illinois at Urbana-Champaign. Permanent Position: Assistant Professor (starting in Fall 2006), Koc University, Istanbul, Turkey. Eric Mortenson, PhD Spring 2003, University of Wisconsin. First Jobs: Postdoc at Max Planck Institute in Bonn, and S. Chowla Research Assistant Professor at Penn State University. Ahmad El-Guindy, PhD Spring 2004, University of Wisconsin. First Job: 3 year Assistant Professor, Texas AM University. Rohit Chatterjee, PhD Spring 2005, University of Wisconsin. VIGRE Fellow. First Job: Analyst, Interactive Brokers, Greenwich, Ct. Holly Swisher, PhD Summer 2005, University of Wisconsin, VIGRE Fellow. First Job(s): Ross Assistant Professor, Ohio State University, Tenure Track Assistant Professor (deferred for Fall 2006), Oregon State University. Present Graduate Students Jackie Anderson, PhD expected in 2006, University of Wisconsin. Lucent Fellow. Karl Mahlburg, PhD expected in 2006, University of Wisconsin. NSF Graduate Fellow. Paul Jenkins, PhD expected in 2006, University of Wisconsin. VIGRE Fellow. Jeremy Rouse, PhD student, University of Wisconsin. NDSEG Fellow. Jayce Getz, PhD student, University of Wisconsin. NDSEG Fellow. Sharon Garthwaite, PhD Student, University of Wisconsin. VIGRE Fellow. Robert Rhoades, PhD Student, University of Wisconsin. NSF Graduate Fellow and NPSC Graduate Fellow. Postdoctoral Advising Scott Ahlgren , 1997-1999. Present Position: Associate Professor, University of Illinois, Urbana-Champaign. Jim Haglund, 1998-1999. Present Position: Associate Professor, University of Pennsylvania and Associate Professor, Ohio State University. Kevin James, 1997-2000. Present Position: Tenure Track Assistant Professor, Clemson University. Matt Papanikolas, 1998-2000. Present Position: Tenure Track Assistant Professor, Texas A M University. David Penniston, 1998-2000. Present Position: Associate Professor, Furman University. Jan Bruinier, 2000-2001. Present Position: Professor, Univ. Cologne. Jeremy Lovejoy, 2000-2003. Van Vleck NSF-VIGRE Assistant Professor. Present Position: CNRS Researcher, Universite Paris (Juissieu), France. Gwynneth Coogan, 2000-2002. NSF PECASE Postdoctoral Fellowship. William McGraw, 2001-2003. Number Theory Foundation Postdoctoral Fellow. Kathrin Bringmann, 2004-present, Van Vleck Assistant Professor. Upcoming Conferences and Business Trips Front Range Number Theory Colloquium, Colorado State University, December 8, 2005. International Conference on Number Theory and Mathematical Physics and SASTRA Ramanujan Prize Presentation, Kumbakonam, India, December 20-22, 2005. Joint AMS-MAA Meetings, Special Session on Arithmetic Geometry, January 12-15, 2006, San Antonio, Texas. Vassar College, Asprey Distinguished Lecturer, Spring 2006. University of Iowa, Distinguished Lecture Series, Spring 2006. University of Arizona, March 9, 2006. Hudson River Undergrad Math Conference, April 8, 2006. MAA Sectional Meeting, April 22, 2006. AMS Special Session, San Franciso, April 29-30, 2006. Conversations in Science, May 10, 2006. NSA, May 13, 2006. MegaMath Meet, UW Madison, May 25, 2006. KAIST, Korea, May 2006. 9th Meeting of the Canadian Number Theory Association, July 9-14, 2006, Vancouver, Canada. Awards and Honors 1995 National Science Foundation PostDoctoral Fellowship 1997 National Security Agency Young Investigator 1998 National Science Foundation CAREER Award 1999 Alfred P. Sloan Foundation Research Fellowship 1999 Louis A. Martarano Professorship, Penn State University 1999 David and Lucile Packard Research Fellowship. 1999 Presidential Early Career Award for Scientists and Engineers. 2001 Prospects in Mathematics Lecture Series, Utah State University. 2002 H. I. Romnes Fellowship. 2003 NSF-CBMS Conference Lecturer. 2003 Milton Brockett Porter Lectures, Rice University. 2003 John S. Guggenheim Foundation Fellowship. 2004 Solle P. and Margaret Manasse Professorship of Letters and Science. 2004 F. Wendell Miller Lecturer, Iowa State University. 2005 National Science Foundation Director's Distinguished Teaching Scholar Award. 2006 Distinguished Visitor (4 lectures), University of Iowa. 2006 Winifred Asprey Distinguished Lecturer, Vassar College. Vitae. Publications. Press releases and stuff. Back to the Dept. Webpage
O'Neil, Catherine
M.I.T. Number theory, Arithmetic algebraic geometry.
mm Please go to my new website at http: www.math.columbia.edu ~oneil
Nebe, Gabriele
Universitt Ulm. Integral representations of finite groups and lattices, orthogonal representations of finite groups and group rings over p-adic integers.
Prof. Dr. G. Nebe RWTH Aachen, LDFM Prof. Dr. Gabriele Nebe Office: Templergraben 64, room 222 Telefon: (0241) 80 - 94545 Fax: (0241) 80 - 92108 E-mail: nebe AT math DOT rwth-aachen DOT de Mailing adress: Lehrstuhl D fr Mathematik RWTH Aachen Templergraben 64 52062 Aachen I am Professor at the Lehrstuhl D fr Mathematik der RWTH Aachen. My research interests are integral representations of finite groups and lattices, orthogonal representations of finite groups and group rings over p-adic integers. My homepage moved. Please update your link: new homepage of Gabriele Nebe
Nicely, Thomas R.
Computations on primes, prime gaps, prime constellations (twins, triplets, and quadruplets) and their reciprocal sums (to extrapolate estimates for the corresponding Brun's constants). Description of the infamous Pentium division bug.
Thomas R. Nicely's Home Page Some Results of Computational Research in Prime Numbers (Computational Number Theory) Thomas R. Nicely http: www.trnicely.net Current e-mail address Description of research Papers and publications Baillie-PSW primality test GNU GMP mpz_probab_prime_p pseudoprimes Most recent counts (10 November 2005) of prime constellations and Brun's constants Table of all known first occurrence and maximal prime gaps Tables of first known occurrence prime gaps Instructions for submitting prime gaps Discovery of the P*ntium FDIV flaw P*ydirt and B*wl B*und Other works Tables of prime counts Tables of twin-prime counts Table of prime quadruplet counts Skewes' problem: Li(N) = pi(N) Silva's record maximal prime gap of 1220 Rosenthal and Andersen's record prime gap of 2254930 The Morain-Alm-Andersen record certified prime gap of 337446 Conjectures of Golomb and Dasgupta E-mail security alert E-mail address display policy Downloads Links NOTE: For simplicity, numbers of very large or very small magnitude, appearing in some documents on this site, are written using the floating-point notation of FORTRAN and C. For example, 5.6e15 means the same thing as 5600000000000000, 5.6*10^15, 5.610^15, 5.61015, 5.61015, etc. DESCRIPTION OF RESEARCH Code written primarily in C, and distributed asynchronously across available personal computers running under extended DOS or W*ndows, is employed to enumerate primes, prime gaps, prime constellations (twins, triplets, and quadruplets) and their reciprocal sums (to extrapolate estimates for the corresponding Brun's constants). Some related computational results obtained by other researchers are also reported here. PAPERS (Unpublished) The Baillie-PSW primality test . Includes GNU C source and executable for implementing both the standard and strong versions of the Baillie-PSW and Lucas-Selfridge primality tests, as well as the extra strong Lucas test. Original posting 10 June 2005. GNU GMP mpz_probab_prime_p pseudoprimes . Counterexamples for the GNU GMP primality testing function. Original posting December 2004. " New evidence for the infinitude of some prime constellations " (20 July 2004). " Enumeration to 1.6e15 of the prime quadruplets " (23 August 1999). " Enumeration to 1.6e15 of the twin primes and Brun's constant " (16 July 1999). " First occurrence of a prime gap of 1000 or greater ," Thomas R. Nicely and Bertil Nyman (21 May 1999). The addendum includes listings of the largest prime gaps (deterministic and probabilistic) found to date. Conjectures of Golomb and Dasgupta . Do n pi(n) and n pi_2(n) take on all sufficiently large positive integer values? Original posting 6 September 2005. PAPERS (Published) " New prime gaps between 1e15 and 5e16 ," Bertil Nyman and Thomas R. Nicely, Journal of Integer Sequences 6 (2003), Article 03.3.1, 6 pp. (electronic). MR1997838 (2004e:11143). Published 13 August 2003. Available in various formats (DVI, PS, PDF, LaTeX) at the home page of the Journal of Integer Sequences . " A new error analysis for Brun's constant ," Virginia Journal of Science 52:1 (Spring, 2001) 45-55, MR 1853722 (2003d:11184). " New maximal prime gaps and first occurrences ," Mathematics of Computation 68:227 (July, 1999) 1311-1315, MR 1627813 (99i:11004). " Enumeration to 1e14 of the twin primes and Brun's constant , " Virginia Journal of Science 46:3 (Fall, 1995) 195-204, MR 1401560 (97e:11014). TABLES OF PRIME GAPS A listing of all first occurrence, maximal, and first known occurrence prime gaps of 1 to 1998 , as well as all other prime gaps exceeding 999 which lie below 5e16. Tables of first known occurrence prime gaps, of measures: 2000 to 3998 . 4000 to 5998 . 6000 to 7998 . 8000 to 9998 . 10000 to 14998 . 15000 to 19998 . 20000 to 24998 . 25000 to 29998 . 30000 to 34998 . 35000 to 39998 . 40000 to 49998 . 50000 to 59998 . 60000 to 99998 . 100000 to 999998 . 1000000 to 999999998 . Note that, due to bandwidth limitations, the above tables display truncated forms of initiating primes which exceed 200 characters in length. The file containing the complete specifications of abbreviated primes, and all recorded first occurrence, maximal, and first known occurrence prime gaps, exceeds 20 MB in size. My presently available bandwidth renders it impractical to maintain this file online and updated. However, I have made available the zipfile merits.zip (171K), which contains a text file specifying the measure G and the merit M=G ln(p_1) for all known first occurrence and first known occurrence prime gaps. This file should be of assistance in determining whether or not some newly discovered gap constitutes a new first known occurrence. The prime gap listings were last updated 0430 EST 12 November 2005. OTHER TABLES An extensive table of pi(x) , the count of primes, with related functions; the domain includes (1e12)(1e12)(5e15). A supplemental table of the count of primes pi(x) , with related functions, for some values of x between 5e15 and 6e15. Toms Oliveira e Silva has computed the most extensive tables of pi(x) of which I am aware. Chris K. Caldwell maintains at his Prime Pages a very extensive compilation of values of pi(x). Xavier Gourdon, Pascal Sebah, and Patrick Demichel have computed the value of pi(x) for some extremely large values of x (e.g., 4e22). An extensive table of pi_2(x) , the count of twin-prime pairs, with related functions; the domain includes (1e12)(1e12)(5e15). A supplemental table of pi_2(x) , for some values of x between 5e15 and 6e15. Toms Oliveira e Silva has computed the most extensive tables of pi_2(x) of which I am aware. An extensive table of pi_4(x) , the count of prime quadruplets, with related functions, to 1.6e15. P*NTIUM FDIV FLAW Original e-mail message announcing the discovery of the P*ntium divison flaw, 30 October 1994. A personal FAQ regarding the P*ntium division flaw. Updated 14 November 2004. An account by Richard M. Smith , President of Ph*r L*p S*ftware, Inc., of the spread of the P*ntium flaw announcement across the Internet during the first few days. pentbug.zip , a zipfile containing the C source code (pentbug.c) and corresponding DOS executable (pentbug.exe) for a program which will check for the flaw. "The P*ntium Division Flaw," Virginia Scientists Newsletter, V:1 (April, 1995), 3. Untitled article concerning the P*ntium division flaw, San Francisco Examiner, 18 December 1994, p. B-5. OTHER WORKS Problem Proposal 1109, Mathematics Magazine 53:5 (November, 1980), 300 (with solution), "When will spring next begin on March 21st in the United States?" "Calculation of the Gregorian Easter cycle," public lecture, October, 1977. The zipfile easter1.zip contains GNU C source code and a DOS Wintel executable for calculating the dates of Easter Sunday. "Special techniques for the solution of a singular integral equation," doctoral dissertation, applied mathematics, University of Virginia, Charlottesville, 1971. Advisor: Gordon E. Latta. "Electronic structure of open-shell doublet-state molecules: application to CN," master's thesis, theoretical physics, West Virginia University, Morgantown, 1965. Advisor: Harvey N. Rexroad. The P*YDIRT and B*WL B*UND football simulation board games (see below). See Downloads for free software. P*YDIRT AND B*WL B*UND The following information is provided in response to numerous inquiries. For most of the period from 1977 to 1995, I carried out design and development for the football simulation board games P*ydirt (pro) and B*wl B*und (college), produced and distributed commercially by Av*lon H*ll Game Company (Baltimore, Maryland) and Sp*rts Ill*strated Enterprises. Commercial support of these games was suspended in April, 1995, and I retired from development in February, 1996. Av*lon H*ll Game Company was later acquired by H*sbro, Inc., and commercial design, production, and distribution of both games was suspended indefinitely. It appears that H*sbro retains the rights to both games at this time. Inquiries regarding these games and their team charts should be directed to Mr. Matt Floray, who has undertaken design, revision, production, and distribution in the interim. Mr. Floray has been in contact with H*sbro, Inc., regarding efforts to bring the games back onto the market. Mr. Floray can be contacted at butchcassidy(at)earthlink(dot)net, or at 213-576-3238. Mr. Floray has access to all the data files, documentation, algorithms, and computer codes that I used to design P*ydirt and B*wl B*und charts from 1977 to 1995, and hopes to produce both new and revised charts for these games. Incidentally, the 1984, 1985, 1986, and 1987 P*ydirt team charts were not my work...despite the fact that my name appears (unauthorized) on many of them. SILVA'S NEW MAXIMAL PRIME GAP OF 1220 Professor Toms Oliveira e Silva reported (14 April 2003) the discovery of a new first known occurrence prime gap of 1220 following the prime 80873624627234849, having merit 31.3370. When Silva completed (20 January 2004) an exhaustive scan of all gaps through 1e17, this gap was proven to be a first occurrence and maximal prime gap. Silva's gap of 1220 is presently the largest known maximal and or first occurrence prime gap, succeeding his previous record maximal gap of 1198. E-MAIL SECURITY ALERT My current e-mail address is always available elsewhere on this site. If you receive an e-mail claiming to be from my address (or some slight variation of my address), which is threatening, abusive, solicitous, commercially oriented, questionable in nature, or otherwise suspicious, treat it as a fraudulent act of vandalism on the part of some third party; ignore its contents and delete it! I DID NOT SEND IT! Be aware that malicious parties and spammers frequently spoof legitimate e-mail addresses, including my own, using forged headers. My own e-mails will always have distinctive identification headers, aside from those inserted by the mail provider. On the rare occasions when I send attachments with e-mails, it will be with the prior permission of the recipient, or there will be a clear explanation within the message of the contents of the attachment. Furthermore, I never include active links, embedded images, J*vaScr*pt, VBScr*pt, or Act*ve-X controls in e-mail (although the mail providers, such as H*tmail, might add such features without my permission). If possible, send your e-mail messages as plain text. Attachments and large data files should be sent as zipfiles (this protects the contents from corruption by the mailers). Please DO NOT send embedded images (jpg, gif, bmp, etc.) in your messages, as these constitute a security hole for viruses and worms, and create a serious bottleneck in e-mail processing. If such images are deemed critical, send them in separate zipped attachments. I have provided detailed instructions for submitting lists of prime gaps. Make sure that your subject line is to the point---otherwise, your message might be deleted, unread, as likely spam. If your zipfiles or other attachments are extremely large (several MB), I do not advise sending them via e-mail. For such extremely large files, provide instead a pointer to a website from which I can download the file. E-MAIL ADDRESSES AND PROPRIETARY MARKS MASKED As a general policy, literal e-mail addresses are no longer published on this site. A few documents have been left unaltered, due to possible historical relevance, in which literal e-mail addresses appear, but it is unlikely (after nearly a decade) that these addresses remain valid. This is part of an effort (probably futile) to hinder the trillions of agencies ceaselessly scouring the Web for e-mail addresses, collecting them for spamming or abusive purposes. This is also the principal reason for the lack of any direct e-mail link to the author. Furthermore, words, symbols, abbreviations, and phrases which I know or suspect to be copyrighted, trademarked, or otherwise legally restricted, have been bowdlerized by replacing key characters with an asterisk (*). DOWNLOADS NOTE: Unless otherwise stated, source code (if provided) is in GNU C, including the GMP library; these applications are distributed as freeware, under the terms of the GNU GPL and FDL licenses . Although developed and tested under extended Wintel DOS in DJ Delorie's DJGPP environment, efforts have been made to maintain portability to other platforms. However, any executables provided have been compiled for the DOS Wintel operating environment. trn.zip , a zipfile (23K) containing the latest revisions of the source code (trn.c) and header file (trn.h) for the support routines called by many of the downloadable applications listed below (some of the applications include their own support files, or are self-contained). Last updated 1830 EDT 24 September 2005. bpsw1.zip , a zipfile (151K) containing the source code, support files, and executable for implementing the standard and strong versions of the Baillie-PSW primality test , as well as the standard and strong Lucas-Selfridge tests and the extra strong Lucas test. Last updated 1830 EDT 24 September 2005. cglp4.zip , a zipfile (155K) containing the source code, support files, and executable for an application which checks prime gaps for validity, using the strong Baillie-PSW primality test . Last updated 1925 EDT 24 September 2005. easter1.zip , a zipfile (56K) containing source code and an executable for calculating the date of Easter Sunday for specified years. Support is provided for both the Western Church (Catholic Protestant) and Eastern Orthodox algorithms, and for both the Gregorian and Julian (Old Style) calendars. No warranty expressed or implied; this code has not been endorsed or approved by any religious institution, organization, or authority. Last updated 0402 EDT 11 June 2005. factor1.zip , a zipfile (131K) containing source files (GNU C with GMP) and an executable for a code which illustrates some algorithms used for factoring integers, including small prime generation, trial divisors, Brent's variation of Pollard's rho method, Pollard's (p-1) method, and a partial implementation of the ECM method. An expression parser is included to allow input in formula form, such as factor1 "2**150 + 1" (see the remark above concerning command-line argument specification). No claim is made that this code is state of the art or research caliber; it is most certainly no threat to current encryption schemes. It may eventually be improved by incorporating additional factoring algorithms. Last updated 1300 GMT 26 January 2005. lirz.zip , a zipfile (83K) containing source, documentation, data files, and an executable for the purpose of computing the number-theoretic functions Li (logarithmic integral); L2, L3, and L4 (Hardy-Littlewood integral approximations); and R(x), Riemann's prime number function formula. Routines are included for GNU C (GCC 3.04, long double precision), UBASIC 8.8f (ultraprecision), and M*thematica 2.1 (ultraprecision). Last updated 0500 GMT 25 April 2004. pentbug.zip , a zipfile (55K) containing the C source code (pentbug.c) and executable (pentbug.exe) for an application which will check for the P*ntium FDIV flaw. Last updated 26 April 2003. pi2.zip , a zipfile (148K) containing the C source codes (pi2e.c and pi2f.c) and executables (pi2e.exe and pi2f.exe) for programs illustrating some practical techniques for generating the twin primes and tabulating their properties. The pi2f code takes advantage of the sieve of Eratosthenes; the pi2e code uses the simple square-root test for primality. The pi2f code is faster in most cases, but either one can enumerate all the twin primes below 1e6 in less than one second on a 600 MHz C*l*ron; pi2f can enumerate all those below 1e8 in under 15 seconds. Last updated 2100 GMT 22 November 2004. pix.zip , a zipfile (209K) containing the C source codes and executables for enumerating the primes and pi(x). Three algorithms are illustrated, using the GMP mpz_probab_prime_p function, trial divisors to the square root, and the sieve of Eratosthenes over byte arrays. Last updated 0100 GMT 29 December 2004. td2k.zip , a zipfile (20K) containing the source code (td2k.ub) and documentation (td2k.txt) for a UBASIC application designed for discovering new first known occurrence prime gaps. This is a fully operational research production code. If you download and use it, I encourage you to notify me of any new first known occurrence prime gaps you discover; I will then post them (with proper attribution and credit) in my lists. NOTE: The input and data files of td2k are incompatible with those of the previous version, td2j. Runs begun with td2j should be completed with td2j, or re-started from scratch with td2k. Last updated 0225 GMT 29 April 2005. UBASIC (725K), a freeware GW-B*SIC-like interpreted programming environment developed by Professor of Mathematics Yji Kida of Rikkyo University, Japan (ftp: rkmath.rikkyo.ac.jp pub ubibm ). UBASIC features easily accessible ultraprecision integer and floating point arithmetic (hundreds of digits), as well as numerous additional intrinsic functions of specific interest in computational number theory. No computational number theorist should be without UBASIC! Also very effective for classroom instructional use. The zipfile provided here contains Version 8.8f (7 October 2000); see also ftp: rkmath.rikkyo.ac.jp pub ubibm . NOTE: Be aware that, due to the peculiar command-line parsing algorithm incorporated in recent versions of M*cr*s*ft W*nd*ws, mathematical expressions in command lines should, to avoid misinterpretation, be specified within DOUBLE QUOTES; e.g., MYCODE "2**150 + 1" This syntax is also valid under DOS and older versions of W*nd*ws, but the double quotes were optional in those operating environments. Depending on the programming language, it may also be necessary (within the source code) to strip off the double quotes and or concatenate command-line arguments. Finally, replacing the exponentiation operator "^" (a particularly troublesome token for W*nd*ws) with "**" (as in FORTRAN COBOL) may be helpful, if the application permits. LINKS Following are some websites of relevance to mathematics in general, and number theory in particular. Note that these pages may open in a new browser window. DISCLAIMER: No endorsement of, or by these sites is expressed or implied, and Thomas R. Nicely accepts no responsibility or liability in consequence of their access or content. Furthermore, no endorsement, expressed or implied, is granted to other sites which link to this site (with or without my authorization), and no responsibility or liability is accepted for the content or access of any external site. The GNU project ("GNU's Not UN*X"), launched in 1984 to develop and provide as free software (under the terms of the GNU GPL and FDL licenses ) a complete UN*X-like operating system, including utilities, applications, and development tools. Linux is one kernel for the GNU operating system. Supported by the Free Software Foundation . DJ Delorie's DJGPP port of the GNU GCC compilers and utilities (including GMP) to the DOS W*ndows platform. This package, including GMP, is also available through Simtel , or from ftp: mirrors.aol.com pub simtelnet gnu djgpp . The GMP (GNU MP) multiple precision software package. Excellent for ultraprecision integer arithmetic; weak on floating point arithmetic and DOS Wintel support. Toms Oliveira e Silva 's projects in computational number theory. The Prime Pages , Chris K. Caldwell, University of Tennessee at Martin. Includes an elementary introduction to prime numbers and number theory. The Number Theory Web , maintained by Keith Matthews, University of Queensland, Brisbane, Australia. MathWorld , a W*lfram Web resource, maintained by Eric W. Weisstein. Steven Finch M*thSoft site at M*thSoft Engineering and Education, Inc. Mathematical constants, unsolved mathematics problems, mathematics puzzles. Mathematical constants and computations . Ultraprecision mathematical constants; very fast and very compact algorithms and codes for the evaluation of certain classical mathematical constants; evaluation of pi(x) for extremely large x ( 1e20). Site maintained by Xavier Gourdon and Pascal Sebah. Sebah also plans to post at this site periodically updated results of his own enumeration of the twin primes and the associated estimates of Brun's constant. Ultraprecision number-theoretical constants . Site maintained by Gerhard Niklasch and Pieter Moree. The Mathematics WWW Virtual Library of Florida State University. The Penn State index of Mathematics Websites around the world. The American Mathematical Society (AMS) . The Mathematical Association of America (MAA) . The Society for Industrial and Applied Mathematics (SIAM) . The Society of Actuaries (SOA) . The Association for Computing Machinery (ACM) . PARI-GP , a software package for computer-aided number theory, including the ultraprecision libpari C libraries and the gp programmable interactive calculator. Targeted at UN*X platforms, with some DOS Wintel support. Site maintained by Henri Cohen and Karim Belabas. The CECM Inverse Symbolic Calculator . TtH , Ian Hutchinson's TeX to HTML translator. NOTICE: I have not been affiliated with L*nchb*rg C*llege since 6 July 2000. Top of page Copyright 2005 Thomas R. Nicely. All rights reserved. This document may be reproduced and distributed for educational and non-profit purposes. Unless otherwise noted, all dates and times on this site are USA Eastern Time (EST=GMT-5 or EDT=GMT-4). Site last updated 0448 EST 12 November 2005.
Nathanson, Melvyn B.
City University of New York. Additive number theory. Contact information and bibliography.
Melvyn Nathanson's Homepage Melvyn B. Nathanson Professor of Mathematics City University of New York, Lehman College and the Graduate Center Mailing address: Department of Mathematics Lehman College (CUNY) 250 Bedford Park Boulevard West Bronx, New York 10468 (718) 960-8860 nathansn@alpha.lehman.cuny.edu List of Books List of Papers
Niziol, Wieslawa
University of Utah. Arithmetic algebraic geometry.
Wieslawa Niziol Wieslawa Niziol MAILING ADDRESS: Department of Mathematics, College of Science, University of Utah, Salt Lake City, Utah 84112-0090 PHONE: 801-581-6851 FAX: 801-581-4148 OFFICE: JWB 101 EMAIL: niziol@math.utah.edu Research Interests Arithmetic algebraic geometry Some Preprints: Crystalline Conjecture via K-theory Semi-stable Conjecture for vertical log-smooth families Cohomology of crystalline smooth sheaves Toric singularities: log-blow-ups and global resolutions
Nagaraj, D.S.
Institute of Mathematical Sciences, C.I.T., Chennai. Algebraic number theory, algebraic geometry.
Nagaraj's page I am interested in the following areas of Mathematics: Algebraic Geometry and Algebraic Number theory. IMSc Brochure Hello. List of publications On the moduli of curves with theta-characteristics Compositio Mathematica,Vol 75, P. 287-297, 1990. The stucture of Iwasawa module associated with a $Z^r_p$-extension of a p-adic local field of characteristic 0 Journal of Number theory,Vol 38,No 1, P. 52-57, May 1991. (with A.R.Aithal) Splitting types of holomorphic bundles associateted to some hormonic maps. Comm. In Algebra Vol 21 (10), P. 3727-3731, 1993. (with S.Ramanan) Polarisation of type (1,2, ... ,2) on Abelian varieties Duke Journal of Mathematics, (Pages, 157 - 194), Vol.80, No.1, Oct.1995. (with C.S.Seshadri) Degenerations of the moduli spaces of vector bundles on curves I Proc.Indian Acad. Sci (Math. Sci.), Vol. 107, No. 2, pp 101-137, May 1997. (with Indranil Biswas) Parabolic ample bundles, II: Connectivity of zero locus of a class of sections Topology, Vol. 37, No. 4, pp. 781-789, 1998. (with Laytimi Fatima) On the Maximal Degeneracy Loci and the secant vector bundle Jour. of Math. Sci.(Newyork) 94 (1999), No.1, 1068-1072. (with C.S.Seshadri) Degenerations of the moduli spaces of vector bundles on curves II Proc. Indian Acad. Sci. (Math. Sci.). Vol. 109, No.2, May 1999. (with V. Balaji, and Indranil Biswas) On the principal bundles over projective manifolds with parabolic structure over a divisor Tohoku Math. J. (2) 53 (2001), no. 3, 337--367. (with V. Balaji, and Indranil Biswas) Principal bundles with parabolic structure Electronic Research Announcements, AMS, Vol. 7, (2001), 37-44. Higher Circular $\ell$-units of Anderson and Ihara Current Trends in Number Theory, 124--128, eds. S.D. Adhikari et al, HBA. New Delhi. (2002). (with S.P.Inamdar) Cycle class map and restriction of subvarieties J. Ramanujan Math. Soc.,17. No.2, (2002), 85-91. (with V. Balaji, and Indranil Biswas) Krull-schmidt reduction for principal bundles. Journal fr die reine und angewandte Mathematik (Crelle's Journal). (To appear). (with V. Balaji, and Indranil Biswas) Ramified $G$-bundles as parabolic bundles Journal of Ramanujan Mathematical Soc., 18(2):123-138, 2003. $\ell$-adic representation attached to an elliptic curve over a number field Elliptic Curves, Modular Forms and Cryptography (HRI Workshop Proceedings) eds.A.K. Bhandari et al,HBA, New Delhi, 167-192, (2003). Seshadri's work on moduli spaces - The case of singular curves A Tribute to C. S. Seshadri eds.V. Lakshmibai et al, HBA, New Delhi, 20-27, (2003). Nef and big vector bundles "Advances in Algebra and Geometry" (University of Hyderabad Conference 2001) Editor C. Musili, HBA, New Delhi, 189-194, (2003). (with B. Sury) The mordell-weil theorem Elliptic Curves, Modular Forms and Cryptography (HRI Workshop Proceedings) eds.A.K. Bhandari et al,HBA, New Delhi, 73-84, (2003). (with B. Sury) On commutativity of rings Journal of Ramanujan Mathematical Soc., 18(2):175-180, 2003. (with B. Sury) A quick introduction to algebraic geometry and elliptic curves Elliptic Curves, Modular Forms and Cryptography (HRI Workshop Proceedings) eds.A.K. Bhandari et al,HBA, New Delhi, 5-32, (2003). Keith Matthews, Number Theory Web Sites: Number Theory Web Hydrabad conf. Pictures(Thanks to D.Keeler) Dec. 2001(7-12): Pic1 IMSc Num-Theory Conf. Pictures Jan. 2002(3-5): Pic2 CAAG-VI at chennai 1--6 Aug 2005: caag Personal Information. Address(Office): Mathematics Section, Institute of Mathematical Sciences, C.I.T. campus, Chennai 600 113. Office: 208. Address (Residence): J-3, Shivani, Block II 40, East Coast Road, Thiruvanmiyur, Chennai 600 041. PHONE(IMSc): (044) 2254 1856 2254 2588 2254 1586; Extn: 291 PHONE(Res) : (044) 2442 1393 FAX(IMSc) : +91-44-2254 1586 TELEGRAMS : MATSCIENCE, Chennai 600 113 E-MAIL : dsn@imsc.res.in. Back to mathematics Back to the IMSc home page
Nekovr, Jan
Universit Pierre et Marie Curie (Paris VI). Algebraic number theory, arithmetic algebraic geometry.
Jan Nekovar Jan Nekov Institut de Mathmatiques de Jussieu Universit Pierre et Marie Curie (Paris VI) Thorie des Nombres, Case 247 4, place Jussieu F-75252 PARIS CEDEX 05 FRANCE Office: 175 rue du Chevaleret 16 rue Clisson, 75013 PARIS (Office: 7A43 ) Tel : 01 44 27 72 83 Fax: 01 44 27 73 21 E-mail: nekovar[at]math[.]jussieu[.]fr URL : http: www.math.jussieu.fr ~nekovar Conference ``p-Adic Modular Forms and Applications", Luminy, 17--21 July, 2006 CV.ps CV.pdf Publications Pictures Courses Links
Nakamula, Ken
Tokyo Metropolitan University. Algorithmic number theory. Home of TNT (Tools for Number Theory) and NZMATH.
Nakamula, Ken Nakamula, Ken Professor, Dr.Sc. Snapshot Illustration Self-Introduction (in Japanese) Effort (in Japanese) Address: 8-667 (Building No.8 indicated by 15 in the map , Room 667) Department of Mathematics Graduate School of Science Tokyo Metropolitan University (TMU) Minami Osawa 1-1, Hachioji Tokyo, 192-0397 JAPAN Email (no reply without from to name in the body of the mail): nakamula AtMark tnt.math.metro-u.ac.jp Fax: +81-426-77-2481 Tel: +81-426-77-1111 (ext 3165 or 3164) Activities: TNT (Tools for Number Theory) Database for Number Theory NZMATH (New SIMATH) System for Number Theory by Python SIMATH System for Number Theory by C JANT (Japan Algorithmic Number Theory) (in Japanese) Research Group AC (Algebra and Computation) Symposium RSNT (Reports of Seminars on Number Theory) (in Japanese) Mailing List Seminars: SEMIKEN (in Japanese) Laboratory of Computational Number Theory SNTTMU (in Japanese) Seminar on Number Theory at TMU Research: Papers under construction Talks under construction Teach: Visiting Hours for Students (in English and Japanese) Lectures (in Japanese) $Date: 2005 08 26 03:15:58 $+ 9:00:00 (JST)
Nakagawa, Jin
Joetsu University of Education. Algebraic number theory: the distribution of the discriminants of algebraic number fields, class numbers of binary forms, zeta functions associated with prehomogeneous vector spaces and Igusa's local zeta functions.
Nakagawa_Homepage [Japanese Version] Jin Nakagawa (Number Theory) I am working in algebraic number theory. In particular, I am interested in the distribution of the discriminants of algebraic number fields in connection with class numbers of binary forms, zeta functions associated with prehomogeneous vector spaces and Igusa's local zeta functions. I intend to apply the results of these research to the study of unramified Galois extensions of algebraic number fields, class numbers of algebraic number fields and Iwasawa theory. Introduction to Algebraic Number Fields Publications Class numbers of pairs of symmetric matrices, Acta Arithmetica 105, 207-225 (2002) On the relations among the class numbers of binary cubic forms, Invent. math. 134, 101-138 (1998) Orders of a quaternion algebra over a number field, J. reine angew. Math. 479, 183-194 (1996) Orders of a quartic field, Memoirs Amer. Math. Soc., No. 583 (1996) Orders of quadratic extensions of number fields, Acta Arithmetica LXVII, 229-239 (1994) Binary forms and unramified An -extensions of quadratic fields, J. reine angew. Math. 406, 167-178 (1990) (Erratum, ibid. 413, 220 (1991)) Binary forms and orders of algebraic number fields, Invent. math. 97, 219-235 (1989) (Erratum, ibid. 105, 443 (1991)) Elliptic curves with no rational points (joint work with K. Horie), Proc. Amer. Math. Soc. 104, 20-24 (1988) On the Galois group of a Number field with square free discriminant, Comment. Math. Univ. Sancti Pauli 37, 95-98 (1988) Class numbers of quadratic extensions of algebraic number fields, Tohoku Math. J. 38, 245-257 (1986) On the Stark-Shintani conjecture and cyclotomic Zp -extensions of class fields over real quadratic fields II, Tohoku Math. J. 36, 439-452 (1984) On the Stark-Shintani conjecture and cyclotomic Zp -extensions of class fields over real quadratic fields, J. Math. Soc. Japan 36, 577-588 (1984) Hobby My hobby is taking photographs of country sides. Top of the page Department of Mathematics Homepage If you have any impressions or advice about this page, please send a mail to jin@juen.ac.jp
Ng, Nathan
University of Georgia. Analytic number theory: the connections between the Riemann zeta function and random matrix theory.
Nathan Ng's Webpage (under construction) Contact Information: Email address: nathan@math.uga.edu Phone: 706-583-0433 Office: Boyd 527A Address: Department of Mathematics University of Georgia Boyd Graduate Students Research Center Athens, Georgia USA 30602-7403 About me: I am a postdoctoral associate and part-time instructor here at the University of Georgia, in Athens, Georgia. My research advisor is Professor Andrew Granville. I received my Ph.D. from the University of British Columbia in fall 2000, under the direction of Professor David W. Boyd. Research: My area of research is analytic number theory. I am currently interested in the connections between the Riemann zeta function and random matrix theory. My Ph.D. thesis, Limiting Distributions and Zeros of Artin L-functions, studied the finer behaviour of prime counting functions and the summatory function of the Mobius function. Teaching: I taught Math 2200 (Calculus) in the fall. However, I am not currently teaching. Links: Here's a link to my very funny office mate : David Hemmer Canadian Broadcasting Corporation: cbc
Nitaj, Abderrahmane
Universit de Caen. Diophantine equations, the ABC conjecture, polynomials, elliptic curves, Szpiro's conjecture.
Abderrahmane Nitaj Abderrahmane Nitaj The abc conjecture Research Interests Ph.D. Thesis Publications Informal Notes Math Links Cultures Contact abc conjecture" The abc conjecture To the abc conjecture home page Back to top Research Interests Number Theory : Diophantine Equations, the abc conjecture, Polynomials. Arithmetic Geometry : Elliptic curves, Szpiro's conjecture. Cryptography : Cryptosystems, The discrete logarithm problem, Elliptic curves. Implementation of Computer Algebra Algorithms : SIMATH , APECS , PARI , MAGMA , MAPLE , UBASIC , LIDIA , CALC , Fractals : (Amateur) Fractal pictures, Animations. Back to top Thesis Consquences et aspects exprimentaux des conjectures abc et de Szpiro (1994). [DVI] [Postscript] Back to top Publications An algorithm for finding good $abc$-examples, Comptes Rendus de l'Acadmie des Sciences de Paris, 317 (1993), pp. 811-815. Algorithms for finding good examples for the $abc$ and the Szpiro conjectures, Experimental Mathematics 3 (1993), pp. 223-230. [Postscript] On a conjecture of Erds on 3-powerful numbers, Bulletin of the London Mathematical Society 27 (1995), pp. 317-318. [DVI] [Postscript] L'algorithme de Cornacchia, Expositiones Math. 13 (1995), pp. 358-365. [DVI] [Postscript] La conjecture $abc$, L'Enseignement Mathmatique 42 (1996), pp. 3-24. [DVI] [Postscript] Aspects exprimentaux de la conjecture $abc$, Sminaire de Thorie des Nombres de Paris, London Math. Soc. 235 (1996), pp. 145-156. [DVI] [Postscript] Dtermination de courbes elliptiques pour la conjecture de Szpiro, Acta Arithmetica 85 (1998), pp. 351-376. [DVI] [Postscript] (With G. Greaves) Some polynomial identities related to the $abc$- conjecture, Gyoery, Kalman (ed.) et al., Number theory in progress. Proceedings of the international conference organized by the Stefan Banach International Mathematical Center in honor of the 60th birthday of Andrzej Schinzel, Zakopane, Poland, June 30--July 9, 1997. Volume 1: Diophantine problems and polynomials. Berlin: de Gruyter (1999), 229-236. [DVI] [Postscript] Invariants des courbes de Frey-Hellegouarch et grands groupes de Tate-Shavarevich, Acta Arithmetica 93 (2000), no. 4, pp. 303-327. [DVI] [Postscript] Isognes des courbes elliptiques dfinies sur les rationnels, J. Computational Math. 4 (2002), 337-448. [DVI] [Postscript] Back to top Informal Notes Petites hauteurs des polynmes par l'algorithme LLL Seminar talk at Cryptography Groupe, Caen. [PDF] , [PS] A Maple Worksheet for elliptic curves This Maple Worksheet gives an explicit model for all elliptic curves defined over Q with a non trivial torsion rational point and for all their isogenous curves associated to isogenies with cyclic kernels consisting of rational points. Le problme du logarithme discret elliptique : Index et Xedni [DVI] , [PS] Le cryptosystme NTRU. [DVI] , [PS] Table of all good abc examples [PDF] , [DVI] , [PS] Table of all good abc-Szpiro examples [PDF] , [DVI] , [PS] Back to top Math Links Number Theory Web (American Site) Mathematics Journals Ecole Polytechnique, GDR MEDCIS Mathematics Software References on Elliptic Curves and Cryptography Back to top Cultures North African Cultures and Adventures The Poet Omar Khayyam The Arabian Nights African Art Samarkand Back to top Contact e-mail address: nitaj@math.unicaen.fr Address: Dpartement de Mathmatiques Universit de Caen Campus II Boulevard Marchal Juin BP 5186 - 14032 Caen Cedex France Back to top
Niklasch, Gerhard
ConSol Software GmbH. Computation of number-theoretical constants.
Gerhard Niklasch's homepage Gerhard Niklasch Just a couple of links for the moment... Since 1998, I have been working for ConSol* Software GmbH , after many years as a research assistant at the Zentrum Mathematik of the Technische Universitt Mnchen. For some mathematical work, jointly with Pieter Moree, see the Number-theoretical constants page . For some glimpses of what I spend my spare hours on, see my Astro-drawings pages (to be extended). G.N. Sat, 01 Nov 2003 20:15:00 MET
Neis, Stefan
Technische Universitt Darmstadt. Computations in algebraic number fields and implementation of algorithms in LiDIA.
Stefan Neis' Homepage Stefan Neis Technische Universitt Darmstadt Fachbereich Informatik Alexanderstr. 10 64283 Darmstadt Germany Degrees: Diploma in Computer Science: Kurze Darstellung von Ordnungen , University of Saarland, Saarbrcken, 1994. Current Work: Computations in Algebraic Number Fields Implementation of algorithms for algebraic number fields in LiDIA . Linear algebra in principal ideal rings ( Technical Report ). Some Interesting Pages in the World Wide Web Navigation in the Internet: AltaVista - The Index of the Internet ( in german ). WWWW - The World Wide Web Worm. Lycos - The Catalog of the Internet. If you dont't know where to go to: try URouLette . If this isn't enough for you: there are many other Search Engines . Cartoons, Pictures: The Farside directory. For geometry fans: A Gallery of Interactive On-Line Geometry (lots of pictures!). Literature and Dictionaries: Gutenberg EText World Wide Web Home Page . An English-German and German-English Dictionary . A French-English Dictionary . Newspapers and magazines: Saarbrcker Zeitung (I especially like the page on janus chess ). Der Spiegel Spektrum der Wissenschaft Star Tribune Electronic Telegraph IWay News On-line CS Techreports Karte deutscher WWW-Server Software: PD-Software from LEO.ORG . Miscellanous Links: The Robert A. Heinlein Home Page . The Hitchhiker's Guide to the Galaxy Homepage Homepage of Thomas Seeling (in german). A multimedia tour through the solar system (there is also the original site in the U.S. ). Fachbereich Informatik in Saarbrcken Lehrstuhl Buchmann
Nair, Kit
University of Liverpool. Ergodic theory; arithmetic. Diophantine approximation and uniform distribution. Harmonic analysis and probability theory.
Dr. R. (Kit) Nair Dr. R. (Kit) Nair Research Interests Ergodic theory; arithmetic. Diophantine approximation and uniform distribution. Harmonic analysis and probability theory. Contact Information E-mail: nair@liverpool.ac.uk Phone: +44 151 794 4057 Fax: +44 151 794 4061 Address: Department of Mathematical Sciences Mathematics and Oceanography Building Peach Street Liverpool. L69 7ZL United Kingdom Some recent publications All articles listed below are published in or will appear in fully refereed publications. Credit for all joint work is to be shared equally with my joint authors. [1] ``On LeVeque's theorem about the uniform distribution (mod 1) of (aj cos aj x )j = 1'', Israel. J. Math. Vol 65, No. 1, 1989, 96-112. [2]``Some theorems on metric uniform distribution using L2 methods'', J. Number Th. Vol 35, 1990, 18-52. [3] ``On strong uniform distribution'', Acta Arith LVI, 1990, 183-193. [4] ``On polynomials in primes and J. Bourgain's circle method approach to ergodic theorems'', Ergod. Th. Dynam. Sys. 11, 1991, 485-499. [5] (with N.H. Asmar)``Certain averages on the a-adic numbers'', Proc. Amer. Math. Soc. Vol 114 No 1, 1992, 21-28. [6] ``On certain solutions of the diophantine equation x- y = p(z)'', Acta Arith LXII.1, 1992,61-71. [7] ``On polynomials in primes and J.Bourgain's circle method approach to ergodic theorems II'', Studia Math 105 (3), 1993, 207-233. [8] ``On the metrical theory of continued fractions'', Proc. Amer. Math. Soc. Vol. 120, No. 4, 1994, 1041-1046. [9] (with A.G. Abercrombie) ``A counter example in the ergodic theory of expanding Markov maps of the unit interval", Mathematics Research Letters Vol. 1, No. 6. 1994, 765-768. [10] ``On Riemann sums and Lebesgue integrals'', Monatsh. Math. (120), 1995, 49-54. [11] ``On an arithmetic property of Lp functions'', Quart. J. Math. Oxford (2) 1996, 101-105. [12] ``On the metrical theory of the optimal continued fraction expansion", Bull. Aus. Math. Soc., vol 56, No. 1, 69-79 (1997). [13] (with A.G. Abercrombie) ``An exceptional set in the ergodic theory of Markov maps of the unit interval, Proc. Lond. Math. Soc., vol 75, (3), No. 1. 221-240, (1997). [14] (with A.G. Abercrombie) ``An exceptional set in the ergodic theory of expanding rational maps", Ergod. Th. Dynam. Sys., vol 17, No. 2, 253-267, (1997). [15] ``On asymptotic distribution on the a-adic integers'', Proc. Ind. Acad Sci. vol 107, No 4, 363-376, (1997). [16] ``On the metric theory of diophantine approximation and subsequence ergodic theory'', New York J. Math., 3 A, 117-128, (1998). [17] ``On uniformly distributed sequences of integers and Poincar recurrence'', Indag. Math. N. S. vol 9, No. 1, 55-63 (1998). [18] ``On the metrical theory of the nearest integer continued fraction expansion', Monatsh. Math., vol 125, No. 3, 241-253 (1998). [19] (with S.L. Velani) `` Glasner sets and polynomials in primes", Proc. Amer. Math. Soc., vol 126, No. 10, 2835-2840, (1998). [20] ``On uniformly distributed sequences of integers and Poincar recurrence II'', Indag. Math., N. S. vol 9, No. 3, 405-415 (1998). [21]``On Hartman uniform distribution and measures on compact spaces", K.A. Ross et. al.(eds), Harmonic Analysis and Hypergroups, 59-75, Trends in Mathematics, Birkhauser (1998). [22] (with M. Weber) ``On variation functions for subsequence ergodic averages'', Monatsh. Math. 128, 131-150 (1999). [23] (with P. Zaris) ``On certain sets of integers and intersectivity'', Proc. Camb. Phil. Soc. 131, no. 1, 157-164 (2001). [24] ``On strong uniform distribution II'', Monatsh. Math, 132, no. 4, 341-348 (2001). [25] (with A. G. Abercrombie) ``On the Hausdorff dimension of certain self-affine sets'', Studia Math., 152, no.2, 105-124 (2002). [26] ``On a problem of R. C. Baker'', Acta. Arith., 109, No. 4, 345-348 (2003). [27] (with H. Kamarul Haili) ``On certain Glasner sets'', Proc. Roy. Soc. Edin. 133A, 849-853 (2003). [28] ``On uniformly distributed sequences of integers and Poincar recurrence III'', Bull. Aust. Math. Soc. 68, 345-350, (2003). [29] (with H. Kamarul Haili)``On the discrepancy of some real sequences'', Math. Scand. (in press). [30] ``On strong uniform distribution III'', Indag. Math. (in press) [31] (with A.G. Abercrombie) ``An exceptional set in the ergodic theory of expanding maps on manifolds", Monatsh. Math. (to appear). [32] (with M. Weber) ``Random perturbations of intersective sets are intersective'', Indag Math. (to appear ). Preprints [33] ``Polynomial ergodic averages and square functions''. [34] ``On vector valued pointwise ergodic theorems'', (7 pages). [35] ``On Tempelman averages and variation functions'', (7 pages). [36] ``On an arithmetic limit on compact groups'', (12 pages.) [37] ``On strong uniform distribution IV'', (12 pages.) Papers by my students while under my supervision not jointly coauthored with me. A.G. Abercrombie: [1] ``Beatty sequences and multiplicative number theory'', Acta. Arith. 70 (1995), no. 3, 195-207. [2] ``Badly approximable p-adic integers'', Proc. Indian Acad. Sci. Math. Sci. 105,(1995), no.2,123-134. [3] ``Reconstructing curves from quantised observations'', Mathematika 42, (1995) no.2 340-353. [4] ``The Hausdorff dimension of some exceptional sets of p-adic integer matrices'', J. Number Th. 53 (1995), no.2 311-341. H.H. Kamarul: [1] ``A metric discrepancy estimate using L2 methods'', ( to appear in the Bulletin of the Malaysian Math. Soc.). S. Kristensen: [1] ``On the metrical theory of the Luroth expansion on the field of formal power series'', (to appear in the Bull. Aust. Math, Soc.). [2] ``On well approximable numbers on the field of formal power series'', (to appear in Proc. Camb. Phil Soc.). [3] ``On badly approximable numbers on the field of formal power series''.
Motohashi, Yoichi
Nihon University. Analytic number theory. Publications.
Small things stir up great said in Arabian Nights, and perhaps in Mathematics as well Yoichi Motohashi Professor of Mathematics, Nihon University Foreign member of the Finnish Academy of Science and Letters Ph.D. (Tokyo University) Ph.D. honoris causa (Turku University) Graduated from Department of Mathematics, Kyoto University, 1966 Enchanted with Analytic Number Theory in boyhood and further via the wonderful encounter with the late Prof. P. Turn (Budapest 1970-72) Office Department of Mathematics Nihon University Surugadai, Tokyo 101-8308 List of academic works English version: yme.pdf Japanese version: ymj.pdf Latest works Uniform bounds for Rankin-Selberg L-functions (with M. Jutila) RS.pdf Smoothed GPY sieve KYT05.pdf Uniform bound for Hecke L-Functions (with M. Jutila): HKLS.pdf (to appear in Acta Mathematica) An overview of Sieve Method and its History : SIEVE.pdf (to appear in Sugaku Expositions AMS) Essays in Japanese Looking back briefly : CST Circular On the wing of prime numbers : Public Talk ************** ZETA WORKSHOPS Theory of the Riemann Zeta and Allied Functions ZETA 2004 Mathematisches Forshungsinstitut Oberwolfach Tagung 19-25 September 2004 Organizers Martin N. Huxley (Cardiff), Matti Jutila (Turku), Yoichi Motohashi (Tokyo), Samuel James Patterson (Gttingen) ZETA 2001 Mathematisches Forshungsinstitut Oberwolfach Tagung 16-22 September 2001 Organizers Martin N. Huxley (Cardiff), Matti Jutila (Turku), Yoichi Motohashi (Tokyo) ********************* Boku-no Family Kazuko and Oran Haruko at Sondershausen [Updated on october 1, 2005] 2005 Yoichi Motohashi
Mihailescu, Preda
Universitt-GH Paderborn. Primality proving; Computational number theory; complex and numerical analysis. Publications, thesis, software: CYCLOPROV, a LiDIA based C++ package for primality proving.
Preda Mihailescu Dr. Preda Mihailescu Research assistant in the research group Algorithmic Mathematics Address: Fachbereich 17 Mathematik Informatik Universitt-GH Paderborn D-33095 Paderborn , Germany Room: D3.244 Phone: +49-5251-603069 Fax: +49-5251-603516 E-mail: preda@uni-paderborn.de You can see some pictures You can still see my old homepage . Research interests: Primality Proving (GIMPS) Computational Number Theory Cryptology Biometry Complex and numerical analysis My Thesis: P.Mihailescu. "Cyclotomy of Rings and Primality Testing", Dissertation, ETH Zurich 1997, Dissertation 12279 ( ps , ps.gz ) Publications: P.Mihailescu. "A Primality test using cyclotomic extensions", in Applied Algebra, Algebraic Algorithms and Error - Correcting Codes, (Proceedings AAECC-6, Rome, July 1988) Lecture Notes in Comp. Sci. 357, Springer Verlag Berlin and New York, 1989, pp. 310 - 323 P.Mihailescu. "Fast Generation of Provable Primes using Search in Arithmetic Progressions", Proceedings CRYPTO 94, Lecture Notes in Computer Science vol 939, Springer 1994, pp. 282-293. A brief description submitted for the IEEE P1363 Cryptographic standard may be downloaded here ( ps , ps.gz ) P.Mihailescu. "Cyclotomy Primality Proving - Recent Developments", Proceedings of the III Applied Number Theory Seminar, ANTS III, Portland, Oregon 1998. Lecture Notes in Computer Science vol xxx, pp y-z. ( ps , ps.gz ) P.Mihailescu. "Recent Developments in Primality Proving" to appear in `High Performance Symbolic Computing' ( ps , ps.gz ) P.Mihailescu, C.Nash. "Some Facts for Lucas - Lehmer Primality Testers", preprint, 1999. ( ps , ps.gz ) P.Mihailescu, F.Morain. "Dual Elliptic Primes and Cyclotomy Primality Proving", presented at the 6-th Conference of the Canadian Society for Number Theory, Winnipeg, 1999 . ( ps , ps.gz ) Some (yet) unpublished material on Catalan's conjecture: P.Mihailescu: "A class number free criterion for Catalan's conjecture", to appear J. of Number Theory. ( ps , ps.gz) P. Mihailescu: "On the class groups of cyclotomic extensions in presence of a solution to Catalan's equation", submitted, J. of N.T ( ps , ps.gz ). P. Mihailescu: "On the class groups of cyclotomic extensions in presence of a solution to Catalan's equation", extended version, interesting, unsubmitted ( ps , ps.gz ). P. Mihailescu: "Primary units and a proof of Catalan's conjecture", submitted Crelle Journal ( ps , ps.gz ) Software: P.Mihailescu: CYCLOPROV . A LiDIA based C++ package for primality proving using cyclotomy. It was used for establishing the current record in general primality proving. It is currently available only for DEC Alpha. Download here together with the required tables . Maybe read the current ` readme ' first. F.Morain: The Elliptic Curve Primality Prover ECPP . Wei Dai: cryptlib , great freeware C++ cryptographic library. From Europe, have a look at : V.Shoup: The NTL long integer library. Usefull links: IFWR-Homepage Francois Morain's ECPP (Elliptic Curve Primality Proving) home page Paul Leyland's Cunningham Project home page The Number Theory List Archives The GIMPS Project home page Chris Caldwell 's GREAT home page on Primes Something about Arumanians ( did you know they exist ? look at me ! ) Care to know how to laugh to the hardships of life ? You might have to learn romanian before, or try with italian first ... or have a look at the more serious french brother. Heart links: Women REALLY Helping street children in Bucharest - Sf. Stelian (I am a member, please ask for more information ) . Fighting against BRAIN DRAINING: The Bucharest - Ecole Normale Superieure Author: Preda Mihailescu last change:
Marklof, Jens
University of Bristol. Quantum Chaos, Equidistribution, Modular Forms. Publications, research projects.
Jens Marklof's home page [enter here]
McMurdy, Ken
Rose-Hulman Institute of Technology. Elliptic curves. Lecture notes, preprints.
Ken McMurdy - RHIT Dept. of Mathematics Ken McMurdy Assistant Professor Department of Mathematics Rose-Hulman Institute of Technology 5500 Wabash Ave. Terre Haute, IN 47803 E-mail: mcmurdy@rose-hulman.edu Phone: (812) 877-8416 Schedule CV Research Personal
Meuser, Diane
Boston University. Number theory and Algebraic geometry. Contact information.
Diane Meuser's Home Page Professor Diane Meuser Office Address: Room 249, 111 Cummington Street, Boston, MA 02215 Office Phone Number: (617) 353-9554 Email Address: dmm@math.bu.edu Office Hours: T 3:00 - 4:30 PM, TH 2:00 AM - 3:30 PM Math Help Hours (in Claflin Hall Lobby): Tuesday Evenings: 7:30 - 10:30 PM Faculty Resident at Claflin Hall, West Campus : My apartment: 1205 Claflin Hall. Phone: 352-0700 Here are some of the things I do: Math Help Ice Cream Parties Ansel Adams Exhibit MA 129 Course Info Special Announcements Course Syllabus Homework Assignments (Posted at the end of each week). Sample Exams Websites of Possible Interest
Macleod, Allan
University of Paisley. Computational number theory, elliptic curves, recreational number theory; High-precision computation of mathematical constants; Special function software. Publications; notes.
Allan's home page ALLAN MACLEOD e-mail: allan.macleod AT paisley.ac.uk (trying to reduce spam, but not working too well!) (The alternating red and black colours are to reflect my lifelong devotion to Inverness Thistle FC, now merged with Inverness Caledonian to form the Scottish Premier League team Inverness Caledonian Thistle) Personal Details Born - 20 November 1953, Inverness, Scotland Married to Jennifer - a music teacher. Four children - Alistair (25), Stuart (23), Catriona (21), and Duncan (18). Current position: Reader in Mathematics Education: 1958-1965 Crown Primary School, Inverness 1965-1971 Inverness Royal Academy 1971-1975 University of Edinburgh, B.Sc. Hons (1st) in Mathematics 1975-1978 University of Edinburgh, Ph.D. in Numerical Analysis Employment: 1978-1979 Medical Computing and Statistics Unit, Edinburgh University 1979-1982 Napier College, Edinburgh (now Napier University) 1982-1986 Scottish College of Textiles, Galashiels (now part of Heriot-Watt University ) 1986-present Paisley College, now University of Paisley Academic Details Responsibilities: Teaching the following modules Topics in Pure Maths Applied Matrix Algebra Sequences and Patterns Maths of Space and Change Departmental Timetabler Science Faculty Timetabler Research Interests: Special function software High-precision computation of mathematical constants Computational number theory, especially elliptic curves as applied to problems in recreational number theory. Publications: Already Published in Journals Electronic Archives Technical Reports Diophantine Notes Last revised: 8 August , 2005
Murty, Kumar
University of Toronto, Canada. Publications and resources for Number Theory courses.
Home Page of V. Kumar Murty Vijaya Kumar Murty Professor of Mathematics University of Toronto 100 St. George Street Toronto, ON M5S 1A1, CANADA E-mail: murty@math.toronto.edu Office: Sidney Smith Hall, Room 4088 Office Hours: By appointment Office Phone: (416) 978-3321 Office Fax: (416) 978-4107 Teaching Publications Journal of the Ramanujan Mathematical Society
Morain, Francois
cole Polytechnique. Computational number theory, cryptography. Papers, ECPP software.
Franois Morain Web page of Franois Morain Version franaise LIX Laboratoire d'Informatique de l' cole Polytechnique quipe Cryptologie My public key. Scientific leader of Projet TANC . E-mail: morain(at)lix.polytechnique.fr 02 03 2005: yet another record for SEA ( 1500 decimal digits ). 18 11 2004: a new record for SEA ( 1000 decimal digits ). fastECPP 27 01 2005 : final version of the article describing fastECPP ( ps.gz , pdf ). 20 07 2004 : 15,071 decimal digits. The announcement ; the certificate . 17 06 2004: the slides of my talk for ANTS-VI (Vermont). 20 12 2003: 10,041 decimal digits. The announcement ; the certificate . A preprint describing the computations. 19 08 2003: the mythical frontier of 10,000 decimal digits is reached by the implementation of J. Franke, T. Kleinjung and T. Wirth, with the primality of 10^9999+33603, whose certificate can be found here . 16 7 2003: 7127 decimal digits. The announcement ; the certificate . The preliminary version of the article . 6 6 2003: 6016 decimal digits. The announcement (updated to take the remarks into account); the certificate . PRIME is in P (august 2002): the original article of Agrawal, Kayal, Saxena; the page of Dan Bernstein. the page of P. Mihailescu containing his amelioration of AKS. My article for the sminaire Bourbaki (in french, .ps.gz , .pdf ); and the slides of my talk (in french, .ps.gz , .pdf ). Fields of Research: Computational Number Theory, Cryptography. Articles My primes The ECPP package release on April 2nd, 2001. Some records in Number Theory Largest known primes: 2^13466917-1 (4 053 946 decimal digits). 2^6,972,593-1 (2,098,960 decimal digits). 2^3,021,377 - 1 (909,526 decimal digits). 2^2,976,221-1 (895,932 decimal digits) Some large certified primes: 10^5019 + 3^2*7^5*11^11 (5020 decimal digits) by Giovanni and Marco La Barbera with PRIMO written by Marcel Martin, 2001. Some large ordinary certified primes: Monoprocessor P5878 (5878 decimal digits) by Jose Luis Gomez Pardo using PRIMO written by Marcel Martin, february 2003. (98*10^4859 - 89) 99 (4859 decimal digits) by H. Rosenthal with PRIMO written by Marcel Martin, 2001. (348^1223 - 1) 347 (3106 decimal digits), proven by Giovanni and Marco La Barbera with Marcel Martin's Titanix program, october 2000. (30^1789-1) 29 (2642 decimal digits), proven by Giovanni and Marco La Barbera with Marcel Martin's Titanix program, october 2000. (2^7331-1) 458072843161 (2196 decimal digits), found by E. Mayer and F. Morain with ECPP , october 1997. Multiprocessor 2177^580+580^2177 (FM, June 6, 2003). Largest composite numbers factored: 2^773 + 1 (233 chiffres dcimaux). (10^211-1) 9 (211 decimal digits) Largest ordinary numbers factored: RSA-155 (155 decimal digits) More links Number theory Keith Matthews's server Prime numbers server Cryptography GRECC Cryptography in France K. S. McCurley's server.
Matthews, Keith
University of Queensland (emeritus). Computational problems, Diophantine equations, LLL, Collatz problem. Originator and maintainer of the Number Theory Web.
Mathematics Disclaimer Mathematics All of UQ News and Events General Information Student Information Staff Information Visitor Information Research Information Club Infinity People Seminars Positions Vacant Sitemap Select a quick link: Other Mathematics Links MathSciNet School of Physical Sciences Faculty of EPSA About UQ my.UQ mySI-net Programs and Courses UQ News UQ Experts UQ Images Organisational Units Staff Web Page You have requested the document http: www.maths.uq.edu.au ~krm . This is a staff web area hosted on a University of Queensland web server. Please be advised that the web pages within this area are NOT officially endorsed by The University of Queensland. The University accepts no responsibility or liability for the contents of this area. This message has been displayed in accordance with the University's Internet Code of Practice , which forms a part of the Handbook of University Policies Procedures . Please note that you will need to enable cookies in your browser in order to proceed. to continue, or to the Mathematics home page. privacy | feedback 2004 The University of Queensland, Brisbane, Australia ABN 63 942 912 684 CRICOS Provider No: 00025B Authorised by: Head of School Maintained by: webmaster@sps.uq.edu.au Last Updated - Today 09:31pm
Mazur, Barry
Harvard University. Number theory, automorphic forms, arithmetic algebraic geometry. Papers and work in progress.
Barry Mazur Homepage Barry Mazur Home page Barry Mazur Resarch Interests Barry Mazur Math Sci papers Barry Mazur Current Projects Barry Mazur Expository articles Barry Mazur Older Material Barry Mazur Curriculum Vitae
Ling San
Nanyang Technological University, Singapore. Applications of number theory to cryptography, coding theory and combinatorial designs.
Professor LING San Professor LING San | Home | Research Interest | Publications | Book Publications | Links | Professor LING San Head, Division of Mathematical Sciences School of Physical Mathematical Sciences Nanyang Technological University E-mail: lingsan@ntu.edu.sg Tel: (+65) 67903753 Fax: (+65) 6316 6984 Educational and Professional Qualifications 1985 B.A., University of Cambridge , UK 1989 M.A., University of Cambridge , UK 1990 Ph.D., University of California, Berkeley , USA Current Service 2004 - present Vice President, Singapore Mathematical Society 2004 - present Secretary, South East Asian Mathematical Society 2004 - present Member, College Advisory Committee, Temasek Junior College 1994 - present Management Committee Member, Breakthrough Missions (drug halfway house), Honorary secretary: 2004 - present Best viewed with Microsoft IE 6.0 and above
Li, Charles
University of California, Los Angeles. Trace formulae. Publications, resources.
Charles Li' Homepage Welcome to Charles Li's Homepage Address: Department of Mathematics, University of California, Los Angeles CA, 90095 U. S. A. Office : MS 6148 E-mail : ccli AT math DOT ucla DOT edu Current Teaching 2005 Spring PIC10A Math My research and publications Online Trace formula resources Links to some number theorists Java List of useful open source software Some java Links Teaching 2005 Winter PIC20A :Link removed. Will be restored after the end of the quarter. 2005 Winter PIC40A 2004 Spring PIC20B class webpage 2004 Fall 285B: Introduction to trace formula
Lauder, Alan
University of Oxford. Algorithmic number theory, with an emphasis on problems related to multivariate polynomials over finite fields.
Alan Lauder Alan Lauder's Web Page I am a university lecturer in the Mathematical Institute, and the tutorial fellow in pure mathematics at Hertford College. I am at present on leave from the former position and hold a Royal Society University Research Fellowship. My interests are in algorithmic number theory, with an emphasis on problems related to multivariate polynomials over finite fields. I can be contacted at "lauder" at "maths.ox.ac.uk". Workshop in Computational Number Theory in Santander, Spain, July 7-9, 2005. Click here I have made some of my work available below. Expository Papers: Rationality and meromorphy of zeta functions, Finite Fields and Their Applications 11 (2005), 491-510. PDF Rigid cohomology and p-adic point counting, to appear in a special issue of JTNB. Postscript Homotopy methods for equations over finite fields, in "Applied Algebra, Algebraic Algorithms and Error-Correcting Codes", Fossorier, Hoholdt and Poli (eds), LNCS 2643,18-24, 2003. Postscript Research Preprints and Publications: (With F. Abu Salem and S. Gao) Factoring polynomials via polytopes, Proceedings of ISSAC (International Symposium on Symbolic and Algebraic Computation) 2004, Gutierrez (Ed), 4-11. postscript . Counting solutions to equations in many variables over finite fields, Foundations of Computational Mathematics Vol. 4 No. 3, (2004), 221-267. Preprint PDF Deformation theory and the computation of zeta functions, Proceedings of the London Mathematical Society, Vol. 88 Part 3, (2004), 565-602. Preprint Postscript (With D. Wan) Computing zeta functions of Artin-Schreier curves over finite fields II, Journal of Complexity, Vol. 20 (2004), 331-349. Postscript Computing zeta functions of Kummer curves via multiplicative characters, Foundations of Computational Mathematics, Vol 3 No. 3, pages 273-295, 2003. Preprint Postscript Zero-patterns of polynomials and convex polytopes, J. of Combinatorial Theory Series A, Vol. 102 (No.1), (2003), 10-15. Preprint Postscript (With D.Wan) Computing zeta functions of Artin-Schreier curves over finite fields, London Mathematical Society JCM Volume 5, (2002), pp 34-55. Preprint Postscript (With R.Brent and S.Gao) Random Krylov spaces over finite fields, SIAM J. on Discrete Mathematics, Vol. 16 No. 2, (2003), 276-287. Preprint Postscript (With D.Wan) Counting points on varieties over finite fields of small characteristic, to appear in ``Algorithmic Number Theory: Lattices, Number Fields, Curves and Cryptography'' (Mathematical Sciences Research Institute Publications), J. P. Buhler and P. Stevenhagen (eds.), Cambridge University Press Preprint Postscript (VERSION: OCTOBER 2002) (With S.Gao and E.Kaltofen) Deterministic distinct-degree factorisation of polynomials over finite fields, Journal of Symbolic Computation, Vol. 38 No. 6, (2004), 1461-1470. Postscript (With K.Paterson) Computing the error linear complexity spectrum of a binary sequence of period 2^n, IEEE Trans. Info. Theory Vol 49 No 1, (2003), 273-280. Preprint Postscript (With S.Gao) Hensel lifting and bivariate polynomial factorisation over finite fields, Math. Comp. 71, No. 240, (2002), 1663-1676. Preprint Postscript (With S.Gao) Decomposition of polytopes and polynomials, Discrete Comput. Geom 26, 89-104 (2001) Preprint Postscript Continued fractions of Laurent series with partial quotients from a given set, Acta Arithmetica XC.3, 252-271 (1999) Preprint Postscript Polynomials with odd orthogonal multiplicity, Finite Fields and Their Applications 4, 453-464 (1998) Preprint Postscript Continued fractions and sequences, Ph.D. London University 1999 Postscript
Lagarias, Jeffrey C.
University of Michigan. Computational Complexity Theory, Cryptography, Diophantine Approximation, Discrete and Computational Geometry, Dynamical Systems, Harmonic Analysis; Mathematical Physics, Optimization, Number Theory. Publications, courses.
Jeffrey C. Lagarias Jeffrey C. Lagarias Professor, Dept. of Mathematics Address: Jeffrey C. Lagarias Department of Mathematics East Hall, Room 3086 University of Michigan Ann Arbor MI 48109 Phone: 734-763-1186 Fax: 734-763-0937 Email: lagarias@umich.edu Research Interests: Computational Complexity Theory, Cryptography, Diophantine Approximation, Discrete and Computational Geometry, Dynamical Systems, Harmonic Analysis. Mathematical Physics, Optimization, Number Theory. Courses Additional Information: Recent preprints Preprints posted on the arXiv, viewable at [http: front.math.ucdavis.edu] Complete publication list in HTML with links to some papers available electronically. Lists of papers organized by subject : (Some papers appear in more than one list.) algorithms computational complexity combinatorial games convex geometry cryptography diophantine approximation and continued fractions discrete mathematics and combinatorial optimization ergodic theory and symbolic dynamics knot theory mathematical programming and optimization neural nets number theory: algebraic and elementary packings and tilings 3x+1 problem and related problems quasicrystals wavelets and fractals zeta functions and related topics Last updated Sept. 1, 2004 (links to papers before 1987 are currently broken)
Lindenstrauss, Elon
Ergodic theory, dynamical systems, and their applications to number theory. Publications.
Elon Lindenstrauss Elon Lindenstrauss My main areas of research are ergodic theory, dynamical systems, and their applications to number theory. For information about my teaching, click here. For a downloadable list of my publications, click here. If you'd like to contact me my email is Phone number: 609 258 4186 Office: Fine Hall 606 Mailing address: Elon Lindenstrauss Department of Mathematics Fine Hall Washington Road Princeton University Princeton, NJ 08544
Long, Ling
Iowa State University. Modular forms for non-congruence subgroups; Modularity of elliptic and K3 surfaces; Arithmetic of Calabi-Yau varieties and applications.
Ling Long
Leibman, Alexander
Ohio State University. Combinatorial number theory. Preprints.
Sasha Leibman - homepage Sasha Leibman - homepage Preprints EPOXIH 1 2
Lim Chong Hai
National University of Singapore. Algebraic number theory.
Lim Chong Hai Dr Lim Chong Hai, PhD (Univ of California, Berkeley) Office S14 - 01 - 07, Dept of Mathematics Tel 6874 - 3336 Fax 6779 - 5452 Email matlimch@nus.edu.sg Mailing Dept of Mathematics, Nat'l Univ of Singapore Address 2 Science Drive 2, Singapore 117543 Lim Chong Hai Department of Mathematics National University of Singapore Singapore 119260 Republic of Singapore matlimch@math.nus.sg Office : S14 01-7 Faculty of Science (65) 6874-6249 (office) (65) 6779-5452 (fax) Back to the home page of the Department of Mathematics Lim Chong Hai matlimch@math.nus.sg Last Modified: 28 July 2003
Liu Jianya
Shandong University. Additive number theory; Automorphic forms; L-functions.
third Jianya Liu Address School of Mathematics System Science Shandong University Jinan, Shandong 250100 P.R. China Tel.: 86-531-8366068 Fax: 86-531-8565182 Email: jyliu@sdu.edu.cn Education B.S: Hebei Normal University, 1984 M.S: Shandong University, 1992 Ph.D: Shandong University, 1995 Research Interests Additive number theory Automorphic forms L-functions Professional Positions 1996-1998, Post-Doctoral Fellow, The University of Hong Kong 1997-1999, Associate Professor, Shangdong University 1999-, Professor, Shandong University 2003-, Cheung Kong Professor of Mathematics, Shandong University 1999-2001, Post-Doctoral Fellow, Lie Group Programme, The University of Hong Kong 2001 Fall, Visiting Professor, The University of Iowa Grants 2001-2003 Trans-Century Training Program Foundation for Talents by the Ministry of Education 2002-2005 The National Science Foundation for Distinguished Young Scholars Publications [26](with Y.B. Ye) Subconvexity for RankinCSelberg L-functions Maass forms, GAFA. 12(2002),1296-1323. [25] (with M.C. Liu and T. Zhan) Squares of primes and powers of 2. II, J. Number Theory 92 (2002), 99-116. [24] (with K.K. Choi) Small prime solutions of quadratic equations, Canad. J. Math. 54 (2002), 71-91. [23] (with Y. Ye) The pair correlation of zeros of the Riemann zeta function and distribution of primes, Arch. Math. (Basel) 76 (2001), 41-50. [22] (with T. Zhan) Distribution of integers that are sums of three squares of primes, Acta Arith. 98 (2001), 207-228. [21] (with T. Zhan) Hua's theorem on prime squares in short intervals, Acta Math. Sin. (Engl. Ser.) 16 (2000), 669-690. [20] (with M.C. Liu)The exceptional set in the four prime squares problem, Illinois J. Math. 44 (2000), 272-293. [19] (with M.C. Liu) Representation of even integers as sums of squares of primes and powers of 2, J. Number Theory 83 (2000), 202-225. [18] (with M.C. Liu and T. Zhan) Squares of primes and powers of 2, Monatsh. Math. 128 (1999), 283-313. [17] (with M.C. Liu and T.Z. Wang) On the almost Goldbach problem of Linnik, Les XXmes Journes Arithmtiques (Limoges, 1997). J. Thor. Nombres Bordeaux 11 (1999), 133-147. [16] (with T. Zhan) The Goldbach-Vinogradov theorem, Number theory in progress, Vol. 2 (Zakopane-Koscielisko, 1997), 1005-1023, de Gruyter, Berlin, 1999. [15] (with T. Zhan) Estimation of exponential sums over primes in short intervals I, Monatsh. Math. 127 (1999), 27-41. [14] (with M.C. Liu and T.Z. Wang)The number of powers of 2 in a representation of large even integers. II, Sci. China Ser. A 41 (1998), 1255-1271. [13] The Goldbach-Vinogradov theorem with three primes in a thin subset, Chinese Ann. Math. Ser. B 19 (1998), no. 4, 479-488. [12] (with M.C. Liu and T.Z. Wang) The number of powers of 2 in a representation of large even integers. I, Sci. China Ser. A 41 (1998), 386-398. [11] (with T. Zhan) Sums of five almost equal prime squares. II, Sci. China Ser. A 41 (1998), 710-722. [10] (with T. Zhan) On a theorem of Hua, Arch. Math. (Basel) 69 (1997), no. 5, 375-390. [9] (with T. Zhan) The ternary Goldbach problem in arithmetic progressions, Acta Arith. 82 (1997), no. 3, 197--227. [8] On an error term of Chowla. III, J. Number Theory 64 (1997), 51-58. [7] On an error term of Chowla. II, J. Number Theory 64 (1997), 36-50. [6] On an error term of Chowla. I, J. Number Theory 64 (1997), 20-35. [5] (with T. Zhan) exponential sums involving the Mobius function, Indag. Math. (N.S.) 7 (1996), 271-278. [4] (with T. Zhan) Estimation of exponential sums over primes in short intervals. II, Analytic number theory, Vol. 2 (Allerton Park, IL, 1995), 571-606, Progr. Math., 139, Birkhauser Boston, Boston, MA, 1996. [3] (with T. Zhan) A Bombieri-type mean-value theorem concerning exponential sums over primes, Chinese Sci. Bull. 41 (1996), 363-366. [2] (with T. Zhan) On sums of five almost equal prime squares, Acta Arith. 77 (1996), 369-383. [1] Remark on a theorem of Wolke, Arch. Math. (Basel) 65 (1995), 413-416.
Li Daxing
Shandong University. The Goldbach conjecture; Cryptography and computer science
third Daxing Li Address School of Mathematics System Science Shandong University Jinan, Shandong 250100 P.R. China Tel: 86-531-8563980 Email: lidaxing@vip.sina.com Education B.S: Shandong University, 1983 M.S: Shandong University, 1985 Ph.D: Shandong University, 1987 Research interests Goldbach Conjecture Cryptography and compter science Professional Positions 1996-1998, Post-Doctoral Fellow, The University of Hong Kong 1997-1999, Associate Professor, Shangdong University 1999-, Professor, Shandong University 2003-, Cheung Kong Professor of Mathematics, Shandong University 1999-2001, Post-Doctoral Fellow, Lie Group Programme, The University of Hong Kong 2001 Fall, Visiting Professor, The University of Iowa Awards () () "" "" Publication [14] , , 1999.11. [13] RSD, , 1999.4. [12] , , 1998.12. [11] Tow notes on low-density subset sum algorithm, Leeture Notes in Computer Science 1994.8. [10] , , 1994.3. [9] Attacks on real polynomial type public-key cryptosystemsand discussion on related problems, Journal of Electronics, 1994.4. [8] , , 1991.5. [7] Cryptosystems with continued fraction algorithm, IEE Electron.Lett., 1991.11. [6] "", , 1991.3. [5] Dickson polynomials Cryptanalysis of Okamoto, IEE Electron.Lett., 1991.2. [4] Lu-LeeCryptanalysis of public-key distribution systems based on, , 1990.10. [3] Cryptanalysis of new modified Lu-lee cryptosystems, IEE Electron.Lett., 1990.9. [2] Euclid, , 1990.6. [1] "", , 1990.1.
Lemurell, Stefan
Chalmers University of Technology Goteborg University. Automorphic forms. Publications, tables of Maass forms.
Stefan Lemurell's Home Page Welcome to Stefan Lemurell's Home Page This is still a rather modest site, but there are some information for students, postscript-files of my research papers and here is a picture of me at the top of Gunung Kerinci the highest mountain on Sumatra. . Computational data on Maass forms can be found here . A collection of personal photos can be found here . Stefan Lemurell sj @ math . chalmers . se Last modified: Thu Nov 3 14:42:42 MET DST 2005 Disclaimer
Lemmermeyer, Franz
Bilkent University. Algebraic number theory, elliptic curves. Papers, lecture notes, texts.
Franz Lemmermeyer
Lapid, Erez
Hebrew University of Jerusalem. Automorphic forms, representation theory, trace formula.
Erez Lapid Erez Lapid Erez Lapid Institute of Mathematics Hebrew University of Jerusalem Jerusalem 91904 ISRAEL Room 310 Manchester Building (Giv'at-Ram), Phone: (972)-2-658-6871 Research Automorphic forms, representation theory, trace formula. Preprints TEACHING CV Lahav and Noam
Logan, Adam
University of Liverpool. Algebraic number theory and elliptic curves; the Brauer-Manin obstruction to rational points on surfaces; Iwasawa theory.
Adam's Home Page Adam Logan's Very Basic Home Page Welcome to Adam's WWW page. May I direct you to my professional page or to my personal page ? If you need to get in touch with me from here: my e-mail address (generally preferred) is adaml@liv.ac.uk . My office telephone number is +1 514 343 6111 ext. 4070, and my office is 4375 pavillon Andre-Aisenstadt. If you want to contact me in some other way, sending e-mail first is probably a good idea. If your preferred mode of communication is the intercontinental ballistic missile , you may get in touch with me at 53 24' 09'' N, 2 58' 41'' W, roughly 20 metres above sea level. (Actually I don't live there any more, but I don't really want ballistic missiles fired at Montreal.) Main pages last updated November 2, 2005 (changes reflecting residence in Montreal and planned move to Waterloo). Any opinions expressed here are mine and not those of the University of Liverpool. Pleidiol wyf i'm gwledydd
Khare, Chandrashekhar
Tata Institute for Fundamental Research. Algebraic number theory. Publications.
Chandrashekhar Khare's Home Page Description of work My interests are mainly in algebraic number theory. One of the basic objectives of algebraic number theory may be said to be to understand the structure of G_Q, the absolute Galois group group of Q. To vary a well-known quote, G_Q knows a lot of number theory and one only has to prevail upon it to reveal all that it knows. For instance the way G_Q knows an elliptic curve E over Q is via its traces in the compatible system of \ell-adic representations attached to it: that the elliptic curve E can be essentially reconstituted from these traces is Falting's isogeny theorem. One way to study a group is via its linear representations. In the case of G_Q there are three possible classes of representations that can be studied: mod p, p-adic and complex. Studying these and their relationships is one important theme in recent work especially after the fundamental work of Wiles on the Shimura-Taniyama conjecture that combined the study of all these three varieties of representations. The one systematic way to construct representations of G_Q is via modular forms. A reciprocity law will say that an abstract representation of G_Q arises automorphically, i.e., it embodies an abstract representation. Such laws are of great importance and have many applications and a long history that neither starts with Artin nor ends with Wiles (to mention just 2 of the key names with reciprocity laws attached to them), as there are many reciprocity laws yet to be proven, and some that are even yet to be formulated! My work is mainly concerned with the relationship between modular forms and Galois representations. Much of it is inspired, either directly or indirectly, by Serre's conjecture (a reciprocity law for mod p Galois representations) that an odd irreducible 2-dimensional mod p representation \rho of the absolute Galois group of Q ``arises from'' newforms. Below I will give a more detailed summary of my work (all references are to the papers listed below): CONGRUENCES: Assuming that \rho does arise from a modular form, it then arises from many. This is the phenomenon of congruences between modular forms. It is of interest to analyse the local behaviour at primes \ell of newforms that give rise to \rho. This was done in the case when \ell is not p in the works of Ribet, Carayol, Diamond and Taylor. The analysis for the \ell=p (or the (p,p)) case is done in the papers [10], [11], [18]. This work is useful in defining the modular deformation rings in work on the Shimura-Taniyama conjecture. The papers [2], [8], [9], [16] are also related to this topic. MOD p DESCENT FOR HILBERT MODULAR FORMS, LIFTING GALOIS REPRESENTATIONS: I considered base change, i.e., restriction, in the context of Galois representations which led to the proof of the existence of a mod p^2 lifting of \rho in [5] where now \rho (just for this sentence) is allowed to be any 2-dimensional mod p representation of the Galois group of the extension K_s K where K_s is a seperable closure of a given field K (see also [1]): this can be phrased by saying that a certain cohomology class is negligible in a terminology introduced by Serre. This work was inspired by the following question: Suppose the restriction of an irreducible odd 2-dimensional mod p representation \rho of G_Q to the absolute Galois group of a totally real cyclic extension of Q is irreducible and modular. Then can this modularity property descended to Q? This is dealt with in [19]. Together with an idea of Taylor, the method of [19] ``reduces'' (sic) proving Serre's conjecture to producing points on certain moduli spaces that are rational over solvable extensions of Q. This has been done in some cases when the image of \rho is small by J. Manoharmayum (GL_2(F_7)) and J. Ellenberg (GL_2(F_9)). A key input in [19] is a result in Galois theory, i.e., a p-adic lifting result of Ravi Ramakrishna for 2-dimensional irreducible representations \rho of G_Q. APPLICATIONS OF SERRE'S CONJECTURE: In [3] it is proven that Serre's conjecture implies the strong Artin conjecture (another reciprocity law) that odd irreducible 2-dimensional representations of the absolute Galois group of Q arise from newforms. This is now known unconditionally in many cases because of Richard Taylor's work carried out in part with several collaborators. In [4] we explore some implications that Serre's conjecture has for finiteness of semisimple mod p representations of G_Q that are unramified outside p. LOCAL LANGLANDS MOD \ELL: In [17] it is proven that the local Langlands correspondence between certain irreducible admissible representations of GL_n(Q_p), and certain n-dimensional representations of the Weil-Deligne group of Q_p defined over $\ell$-adic fields, ``reduces mod \ell'' (\ell unequal to p). This reproves some results of M.-F. Vigneras by different methods that are more global and which use the theory of congruences between automorphic representations, besides using the compatibility proved in the work of Harris and Taylor between the global and local Langlands correspondence. The methods of [17] have been subsequently used by Vigneras to give a complete proof of the mod \ell local Langlands correspondence. p-ADIC GALOIS REPRESENTATIONS: In [23] finiteness results are proved for Selmer groups attached to p-adic lifts of even irreducible 2-dimensional mod p representations that are produced by Ravi Ramakrishna. In [21] converging sequences of Galois representations are constructed and studied. In [22] ramification properties of semisimple p-adic representations of Galois groups of number fields are studied. MODULARITY THEOREMS: In [24] new proofs are given of the modularity lifting theorems of Wiles, Taylor-Wiles that use the auxiliary primes discovered by Ravi Ramakrishna. COMPATIBLE SYSTEMS OF MOD p GALOIS REPRESENTATIONS: In [7], [26], [27] we consider Galois representations in different characteristics and examine reciprocity laws in this context. In [28] a geometric analog of this is considered. I will describe the contents of the papers listed below that are still in preparation: The question that is addressed in [28] (suggested by the work of Rodriganz and Schoof (J. of Number Theory 64 (1997), 276--290) and the preprint ``Compatible systems of mod p Galois representations II'' below) is: Suppose A is an abelian variety over the rationals Q, and f:A(Q) ------- A(Q) is a homomorphism of the Mordell-Weil group of $A$ that ``reduces mod p'' for almost all p. Then does the restriction of f to a subgroup of finite index of A(Q) arise from an endomorphism of A? In many cases we answer this question. A similar question can be posed and answered more easily for arithmetic lattices in linear groups. In [27 ] we explore mod pq versions of Serre's conjecture: this was considered earlier by Barry Mazur and Ken Ribet, and there are computations of William Stein related to it. It was also considered in the paper ``Mod p descent for Hilbert modular forms'' below. In these earlier studies the ``level aspect'' was studied while here we emphasise the ``weight aspect''. We also consider mod pq 1-dimensional Galois representations and study when they arise simultaneously from a Hecke character. In [25] we study the following question: Let N be an integer prime to a given prime $p$. A Hecke eigensystem that arises from H^1(\Gamma_1(N),F_p) also arises from H^1(\Gamma_1(N),Symm^{p-1}(F_p)). This is puzzling as the SL_2(F_p)-module Symm^{p-1}(F_p) does not admit F_p as a subquotient. We ``resolve this puzzle'' and explore the group theoretic meaning of the Hasse invariant in a few different settings. My papers are here:
Karatsuba, Anatolii Alexeevich
Steklov Institute of Mathematics and M. V. Lomonosov Moscow State University. Analytic number theory; mathematical cybernetics.
Karatsuba Anatolii Alexeevich Russian page head of DepartmentofNumberTheory, SteklovInstitute ofMathematics of RussianAcademyofSciences , professor of Department "MathematicalAnalysis" , Faculty ofMechanics andMathematics , M.V.LomonosovMoscowStateUniversity(MSU) Address: Department of Number Theory, SteklovInstitute ofMathematicsRAS 8,Gubkinastr., 119991, Moscow, Russia Tel.: (095)9383732 Fax: (095)1350555 Email: karatsuba@mi.ras.ru Born 31.01.1937, Grozny Scientific interests Education and Professional Activities Prizes and Awards List of Research Works The paper: G.I.Archipov, V.N.Chubarikov "On the mathematical works of professor A.A.Karatsuba" (Proc. Steklov Inst. Math., vol. 218,1997). Top Scientific interests and works are in the field of analytic number theory and mathematical cybernetics: 1. Theory of trigonometric sums and trigonometric integrals: the Tarry problem the p-adic method multiple trigonometric sums estimating the Hardy function in the Waring problem the Artin problem on local representation of zero by a form the Hua Loo Keng problem on the index of convergence of the singular integral in the Tarry problem estimating the short Kloostermans sums a multidimensional analogue of Waring's problem 2. Theory of the Riemann zeta function: the Selberg problem zeros of linear combinations of L -series of Dirichlet distribution of zeros of the Riemann zeta function on the short intervals of the critical line the bound of zeros of the Riemann zeta function and the multidimensional Dirichlet divisor problem lower bounds for the maximum modulus of zeta function in small domains of the critical strip and in short intervals of the critical line the behavior of the argument of zeta function on the critical line 3. Theory of the Dirichlet characters: estimating sums of characters in finite fields estimating linear sums of characters in shifted prime numbers estimating sums of characters of polynomials with prime argument lower bounds for the sums of characters of polynomials sums of characters on additive sequences distribution of power residues and primitive roots in sparse sequences 4. Theory of finite automata: the problem of sharp estimate of the least length of the experiment determining the state of the automaton in the end of the experiment 5. Theory of fast computations: the first general method and algorithm for fast multiplication of multiplace numbers the "divide and conquer" method which had served as the source of a new direction of investigations connected with fast computations the complexity of the computation of the functions. Top Education and Professional Activities 1959 graduated from Faculty of Mechanics and Mathematics of M.V.Lomonosov Moscow State University(MSU) with the speciality "Mathematics". Place of employment: Faculty of Mechanics and Mathematics of MSU from February of 1962 till the present time, from1966 as co-employment. The main place of employment from 1966: Steklov Institute of Mathematics of Russian Academy of Sciences (MIAN) , senior scientific researcher, leading scientific researcher, head of Department of Number Theory from 1983 till the present time. Cand. Sci. (Ph.D.) in Mathematics (1962): Ph.D. thesis: "Rational trigonometric sums of a special form and their applications", scientific advisor: professor N.M.Korobov Dr. Sci. (Habilitation) thesis (1966): "Method of trigonometric sums and the theorems on the mean value". The certificate of professor in Department "Theory of Numbers" (1970), professor of Department "Mathematical Analysis" from1980 till the present time. Member of the specialized Doctor's Councils of Faculty of Mechanics and Mathematics of MSU and of MIAN . Member of the Expert Committee of Russian Academy of Sciences (RAS) on the A.A.Markov award and the I.M.Vinogradov award. Member of editorial boards of the journals "Izvestiya: Mathematics" , "Mathematical Notes" , "Mathematica Slovaca" . Lecturer and head of the research seminars at Faculty of Mechanics and Mathematics of MSU from 1962 till the present time. Supervisor of 15Ph.D. students (Ph.D. degrees in Mathematics obtained from Moscow State University and the Steklov Institute), 7of them later obtained D.Sci. Habilitation degree. Top Prizes and Awards The P.L.Chebyshev award of ANUSSR (1981), the I.M.Vinogradov award of RAS (2001), Meritorious Science Worker of Russia (1999). Top
Keating, Jon
University of Bristol. Links between the semiclassical asymptotics of wave quantum mechanics and chaos in classical Hamiltonian mechanics, connections with asymptotic problems in number theory.
Jonathan P. Keating Home Publications Mathematics Home Position: Professor of Mathematical Physics and EPSRC Senior Research Fellow Contact details: School of Mathematics, University of Bristol, University Walk, Clifton, Bristol. BS8 1TW Telephone: +44 (0)117 928 7975 Fax: +44 (0)117 928 7995 email: j.p.keating (add @bristol.ac.uk) Research Interests: Quantum chaos, random matrix theory, number theory.
Kou, Ming
University of Illinois at Urbana. Analytic number theory and probability.
Ming kou's homepage in math department UIUC Welcome to my homepage! Math 118 B1 I'm currently (Fall, 2005) doing research in Probability theory (SLE). Advisor: Robert Bauer Email: mingkou@uiuc.edu or mingkou@math.uiuc.edu (For school related materials) qdcn2008@yahoo.com (For personal and other, especially Chinese characters and images) Mailing address: Ming Kou Department of Mathematics University of Illinois Urbana, IL,61801 USA Some links: If you are an ordinary people like me, you can broadcast your password through the net by using telnet: Check your UIUC E-mail or here if the other link doesn't work. If you are a VIP, use: webmail or ssh. Check your Yahoo mail Check your hotmail Go to UIUC homepage Go to Math. Department For more, go to my Personal Page ( coolm.org ).
Kassaei, Payman
McGill University. Arithmetic algebraic geometry, modular forms. Publications, talks, teaching material.
Homepage of Payman Kassaei Payman L Kassaei (Ph.D. in mathematics, M.I.T.) Visiting Professor Dept of Math McGill University Montreal, QC H3A 2K6, Canada Office: Burnside 1125 Emails: kassaei[@]math[.]mcgill[.]ca kassaei[@]alum[.]mit[.]edu (Permanent Email Address) Phone: 514-398-3831 Fax: 514-398-3899 Professional Personal Research Teaching Math Links Pictures Uttered by others! This homepage is yet to grow!
Knapp, Michael
Loyola College. Diagonal forms, Artin's conjecture. Papers, preprint, thesis.
Mike Knapp's Home Page Michael Knapp Mathematical Sciences Department Loyola College 4501 North Charles Street Baltimore, MD 21210-2699 Office: Knott 301e Office Hours: Monday 2-3 Wednesday 2-4 Friday 2-3 Or by appointment. Phone: (410)-617-2382 Email: mpknapp (at) loyola.edu About Me Math 251 Webpage Math 251 Webwork Math 395 Webpage Math 490 Webpage Other Teaching Stuff Research Description (Non-technical) Papers and Preprints Fall Schedule Professional Items Welcome to my home page. I'm glad you stopped by! I am currently an assistant professor in the mathematical sciences department at Loyola College in Baltimore. I came here in August 2003 from the University of Rochester , where I taught and did research for three years. Before that, I was a student at the University of Michigan , earning my Ph.D. under the direction of Trevor Wooley . My research interests are in number theory. One of the main reasons why I like number theory is that there are so many questions which any junior high school student can understand, but nobody in the world knows how to answer. If you are interested, you can check out my research description above. My personal research is unfortunately not on one of the questions that are really easy to state, but I have tried to write it in a way so that it's not too hard to understand. I hope that I have succeeded. If you're interested in reading a more detailed account of my work, please read either my research statement and NSF grant application on the professional items page or my papers and preprints. This fall, I'm teaching Math 251 (Calculus I), Math 395 (Discrete Methods) and Math 490 (Special Topics - Topology). You can find links to the homepages for these courses above, as well as some information about other courses I have taught. This year, I am also in charge of Loyola's Putnam Exam and Virginia Tech Math Competion teams. These are math contests for college students. The problems can be very hard (especially the Putnam exam - the Va. Tech problems are somewhat easier), but the contest is a lot of fun. If you are interested in participating, please contact me! I'm an uncle! My first niece, Samantha Nicole Knapp, was born on June 16, 2003. Click here for pictures! Last major update: August 26, 2003.
Khadjavi, Lily S.
Loyola Marymount University. Algebraic number theory; the ABC conjecture; cryptography, dessins d'enfants, complexity theory. Publications.
Lily S. Khadjavi's Home Page Lily S. Khadjavi "The universe... is written... in the language of mathematics." - Galileo Office: University Hall 2718. Also known as 1000e, give or take. Postal Address: Lily Khadjavi Department of Mathematics Loyola Marymount University One LMU Drive, Suite 2700 Los Angeles, CA 90045 Telephone: 310-338-5969 Fax: 310-338-3768 Email address: lkhadjavi@lmu.edu If all else fails, you can try me at khadjavi@post.harvard.edu. You can find me in the Loyola Marymount University math department . Office hours: Mondays 10-11, 4-5 Wednesdays 4-5 Thursdays 1-3 and by appointment In general, if you have a question, you should simply come by and see me! Classes, Spring 2004 Math 123-section 1, MWF at 2pm, University Hall 2330 Math 123-section 2, MWF at 3pm, University Hall 2330 Math 331, MWF at 11am, University Hall 2327 Education: Ph.D. U.C. Berkeley A.B. (same as a B.A.) Harvard University curriculum vitae in pdf format Research in number theory: attacking the ABC Conjecture! Co-conspirator: Victor Scharaschkin Elliptic curves and the ABC Conjecture (preliminary version) And some other papers: Belyi maps and elliptic curves with V. Scharaschkin. An effective version of Belyi's Theorem . Useful links: Number Theory Web maintained by Keith Matthews Math ArXiv mirror site at UC Davis Summer research programs (REUs) for students in mathematics Other interests include cryptography, dessins d'enfants, complexity theory, and quantitative methods social justice. Racial profiling in Los Angeles: A paper concerning motor vehicle stop and search data is in progress. Some more useful links: The LAPD Consent Decree: overview and public reports. Data for January to June of 2004 expected in September. Northeastern University's Racial Profiling Data Collection Resource Center. Alene for deg Der braender et lys i natten, det braender alene for meg, og puster jeg til det, saa flammer det op og flammer alene for meg.-- Men taler du stille, og hvisker du tyst, er lyset plutselig mere enn lyst og braender dypt i mitt eget bryst --alene for deg.-- Tove Ditlevsen (orig. Danish) (fra Pigesind, dikter utkom i 1939) Some words to live by, from my most wonderful family in Norway: Det finnes ikke daarlig vaer, bare daarlig klaer. And finally, once you've tasted raw herring in the Netherlands, you really can't ask for anything more (except maybe a fresh stroopwafel for dessert): Alleen gekken en dwazen schrijven hun naam op de deuren en glazen.
Katz, Nicholas M.
Princeton University. Number theory and algebraic geometry. Publications, photographs.
Nicholas M. Katz's Home Page Check out monodromy.com Bibliography of Nicholas M. Katz pdf file (83 KB) C.V. of Nicholas M. Katz pdf file (22 KB) Photo from 60'th Birthday Conference jpg file (807 KB) Photo from 60'th Birthday Conference (high resolution version) TIF file (123 MB) V-Strom DL650 suspension adjustment Nicholas M. Katz PDF and DVI files available for download E-polynomials, zeta-equivalence, and polynomial-count varieties (appendix to a paper of Rodriguez-Villegas and Hausel) dvi file (30 KB) pdf file (550 KB) G_2 and hypergeometric sheaves (revised Sept. 30, 2005) dvi file (204 KB) pdf file (4484 KB) On a question of Lillian Pierce dvi file (44 KB) pdf file (982 KB) Hooley parameters for families of exponential sums over finite fields pdf file (122KB) Notes on G_2, determinants, and equidistribution (typo's corrected Dec. 9, 2003) pdf file (213KB) online version (joint with Esnault) Cohomological divisibility and point count divisibility (corrected version of nov. 10, 2003) dvi file (41 KB) pdf file (187 KB) Corrected version of Chapter 5 of "Twisted L-Functions and Monodromy" pdf file (201KB) Moments, Monodromy, and Perversity: a Diophantine Perspective Corrections to "Space filling curves over finite fields" dvi file (12 KB) pdf file (88 KB) (joint with Pandharipande) Inequalities related to Lefschetz pencils and integrals of Chern classes pdf file (80 KB) Estimates for "nonsingular" multiplicative character sums dvi file (60 KB) pdf file (206 KB) A semicontinuity result for monodromy under degeneration dvi file (36 KB) pdf file (163 KB) Sato-Tate Equidistribution of Kurlberg-Rudnick Sums pdf file (94 KB) AWS2000 Lectures: L -functions and monodromy: four lectures on Weil II pdf file (184 KB) Larsen's Alternative, Moments, and the Monodromy of Lefschetz Pencils pdf file (201 KB) Sums of Betti numbers in arbitrary characteristic pdf file (83 KB) Frobenius-Schur indicator the ubiquity of Brock-Granville Quadratic Excess pdf file (93 KB) Twisted L-Functions and Monodromy (whole book) pdf file (909 KB) Twisted L-Functions and Monodromy (introduction only) pdf file (95 KB) (joint with de Jong) Monodromy and the Tate Conjecture:Picard numbers and Mordell-Weil ranks in families pdf file (181 KB) Corrections to Katz-Sarnak pdf file (78 KB) Corrected version of 6.16.6 in Katz-Sarnak pdf file (75 KB) Subject index to Katz-Sarnak pdf file (44 KB) Notation index to Katz-Sarnak pdf file (73 KB) Nicholas M. Katz books on Amazon In association with Amazon.com Buy Twisted L-Functions and Monodromy in hardback Buy Twisted L-Functions and Monodromy in paperback Buy Katz-Sarnak Buy Exponential Sums and Differential Equations in paperback Buy Rigid Local Systems in hardcover Buy Rigid Local Systems in softcover Buy Katz-Mazur Search for Exponential Sums and Differential Equations in hardback Search for Gauss Sums, Kloosterman Sums, and Monodromy Groups in hardcover Search for Gauss Sums, Kloosterman Sums, and Monodromy Groups in softcover Buy TurboTaxDeluxe Buy New Joys of Yiddish
Kedlaya, Kiran
Massachusetts Institute of Technology. Research primarily in algebraic geometry and number theory. Papers and preprints, mathematics links, and contact information.
Kiran S. Kedlaya Kiran Sridhara Kedlaya The only thing we have to fear is fear itself--nameless, unreasoning, unjustified terror which paralyzes needed efforts to convert retreat into advance. -- Franklin D. Roosevelt E.g., um, Iraq? -- topical anagram I am an Assistant Professor of Pure Mathematics at MIT . My research is primarily in algebraic geometry and number theory (including algorithmic computational questions); effective July 1, 2004, I am supported by NSF grant DMS-0400727 . During the fall 2005 semester, I am teaching 18.014: Calculus with Theory . I am also a co-organizer of the Harvard-MIT Algebraic Geometry Seminar , and of the Brandeis-Harvard-MIT-Northeastern Joint Mathematics Colloquium . For more about me, see below . This site is larger than you might expect; try the navigation bar and the site map for getting around. Enjoy! Kiran S. Kedlaya Department of Mathematics , Room 2-165 Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139-4307 USA phone: (617) 253-2946 (on campus, 3-2946) Office hours: Wednesday 12:30-1:30 email: kedlaya[at] either of mit[dot]edu or math[dot]mit[dot]edu Beware that I do not always acknowledge unsolicited emails. Click for further contact info and weekly schedule . Most useful content 18.014 (Calculus with Theory) home page (fall 2005) Contact information Curriculum vitae Itinerary Papers and preprints Photos Professional content Site map STAGE (arithmetic geometry seminar) Weekly schedule Other content 18.786 (Topics in Algebraic Number Theory) home page (spring 2006) Mathematics links Course web pages Seminar web pages Off-site content I maintain Personal content News Announcements No news right now; check back later. A bit about me I became an Assistant Professor of Pure Mathematics here at MIT as of July 1, 2003. My previous appointment was an NSF Postdoctoral Fellowship at UC Berkeley . For more personal details, see my biography . My research interests tend to concentrate in algebraic geometry and algebraic number theory, with the odd foray into combinatorics. More precisely, I've been interested in p-adic methods in algebraic geometry, such as F-crystals and Monsky-Washnitzer cohomology. (But I can't resist the occasional nice elementary question.) For more details, see my research statement or my notes for potential doctoral advisees . This page has been visited times since the counter was last reset, or 2 Apr 2003, whichever is more recent. These pages should be properly viewable using any browser , and make no use of frames. In particular, they should be HTML 4.01 Transitional compliant. (For instance, click here to verify that this page is valid.) If you find this not to be the case, please let me know. Home | Contact | Curriculum vitae | Itinerary | Papers | Personal | Photos | Professional | Site map
Kiming, Ian
University of Copenhagen, Denmark. Recent paper in downloadable formats.
Ian Kiming's Home Page Recent papers: New models for the action of Hecke operators in spaces of Maass wave forms: pdf (with H. Verrill): On modular mod $\ell$ representations with exceptional images. J. Number Theory 110 (2005), 236--266. Preprint version: pdf (with P. Frederiksen): Galois representations of dihedral type over ${\mathbb Q}_p$. Acta Arith. 111 (2004), 43--59. Preprint version: pdf (with C. Khare): Mod $pq$ Galois representations and Serre's conjecture. J. Number Theory 98 (2003), 329--347. Preprint version: pdf Fermat's sidste stning: En oversigt. (Survey article, in Danish): pdf Om kongruenstal. (Survey article, in Danish): pdf Current course: Matematisk Metode. Previous courses and notes ... Contact: Ian Kiming Universitetsparken 5, DK-2100 Copenhagen Oe, Denmark Tel. (Work): 3532 0758 Tel. (Home): 4369 5660 email: Misc.: Om forskning.
Kani, Ernst
Queen's University, Kinston, Canada. Arithmetic Geometry. Includes preprints, publication, and presentations (dvi and pdf format).
Ernst Kani's homepage Internal Users | Site Map | Math and Stats | Queen's University | t Queen's Math. Stats - Ernst Kani's Home Page Ernst Kani E-mail: kani@mast.queensu.ca Web: http: www.mast.queensu.ca ~kani Mailing Address: Department of Mathematics, Jeffery Hall, 99 University Avenue, Queen's University, Kingston, Ontario, K7L 3N6, Canada Office: Jeffery Hall, Room 211 Office Phone: (613) 533-2435 Office Fax: (613) 533-2964 Degrees B.Sc. (University of Toronto) M.Sc. (University of Toronto) Dr. rer. nat. (University Heidelberg, Germany) Office Hours (Fall 2004) Mon 13:30-14:30, Wed 12:30-13:30, Thurs 14:30-15:30, (in Room 211, Jeffrey Hall) Courses (Fall Winter 2005 06) Math 211: Algebraic Methods Math 918: The Arithmetic of Modular Forms II Math 418 818: Number Theory and Cryptography (Winter 2006) Research Interests Key words: Arithmetic (Diophantine) Geometry; elliptic curves, abelian varieties, Galois representations, modular forms, moduli problems, Hurwitz spaces, curves of genus 2. Summary: My main research area is Arithmetic Geometry, which is a synthesis of Number Theory and Algebraic Geometry, and which includes the realm of Diophantine questions such as Fermat's Last Theorem. In addition, I am interested in applications of Arithmetic Geometry to Public Key Cryptography. More precisely, my research focuses on Galois representations, particularly those attached to (modular) elliptic curves; these played a crucial role in Wiles' proof of Fermat's Last Theorem. The question of when such representations can be isomorphic is of special interest to me, for a precise understanding of this question would have important Diophantine consequences, as G. Frey (Essen) has observed. This leads to four inter-connected yet separate lines of investigations: 1) Modular Diagonal Quotient Surfaces, which classify such isomophisms; 2) Curves of genus 2 with elliptic differentials, which are obtained by fusing together two elliptic curves with isomorphic Galois representations (in part joint work with G. Frey); 3) Hurwitz schemes arising from genus 2 covers over elliptic curves. 4) Representations of fundamental groups (in part joint work with G. Frey and H. Volklein). The above topics, particularly the modular diagonal quotient surfaces, are also closely related to following topic(s): 5) Modular forms and Galois representations Recent Preprints Abelian subvarieties and the Shimura construction. (Revised) Aug. 2005, 25pp. Abstract: pdf file Preprint: dvi file or pdf file. Endomorphisms of Jacobians of modular curves (revised) Aug. 2005, 12pp. Abstract: (not available) Preprint: dvi file or pdf file. The number of genus 2 covers of an elliptic curve Dec. 2003, 31pp. Abstract: (not available) Preprint: dvi file or pdf file. The modular degree and the congruence number of a weight 2 cusp form (with A.C. Cojocaru) Sep. 2003, 9pp. (has appeared in Acta Arithmetica) Abstract: (not available) Preprint: dvi file or pdf file. The surjectivity of mod m Galois representations (4pp.). Appendix to: The surjectivity of the Galois representations associated to non-CM elliptic curves by A.C. Cojocaru. March 2003, 15pp. (has appeared in Bull. Can. Math. Soc.) Abstract: (not available) Preprint: dvi file or pdf file. Hurwitz spaces of genus 2 covers of elliptic curves. (has appeared in Collectanea Math.) See also: IEM Preprint No. 9 (2001), IEM (Essen), June 2001, 55pp. Abstract: pdf file Preprint: dvi file or pdf file. Mazur's question on mod 11 representations of elliptic curves (with O. Rizzo). Dec. 2000, 22pp. Abstract: pdf file Preprint: dvi file or pdf file. Selected Publications The modular degree and the congruence number of a weight 2 cusp form (with A.C. Cojocaru) Acta Arith. 114 (2004), 159-167. Preprint: dvi file or pdf file. Hurwitz spaces of genus 2 covers of elliptic curves. Collect. Math. 54 (2003), 1-51. See also: IEM Preprint No. 9 (2001), IEM (Essen), June 2001, 55pp. Abstract: pdf file Preprint: dvi file or pdf file. Projective p-adic representations of the K-rational geometric fundamental group (with G. Frey). Archiv der Mathematik 77 (2001), 32-46. Preprint: dvi-file or pdf-file Curves with infinite K-rational geometric fundamental group (with G. Frey and H. Volklein). In: Aspects of Galois Theory - Proceedings of the Conference on Galois Groups 1997, University of Florida, Gainesville, Florida. (H. Volklein , D. Harbater, P. Muller, J. Thompson, eds.) London Math. Soc. Lecture Notes 256 (1999) 85-118. Preprint: dvi-file or pdf-file Modular diagonal quotient surfaces (with W. Schanz), Mathematische Zeitschrift 227 (1998) 337--366. Preprint: dvi-file or pdf-file Diagonal quotient surfaces (with W. Schanz), Manuscripta Mathematica 93 (1997) 67-108. Preprint: dvi-file or pdf-file The existence of curves of genus 2 with elliptic differentials, J. Number Theory 64 (1997) 130-161. Preprint: dvi-file or pdf-file The number of curves of genus 2 with elliptic differentials, J. reine angew. Math. 485 (1997) 93-121. Preprint: dvi-file or pdf-file Fermat's Last Theorem (Coleman-Ellis Lecture, November 1996), Queen's Mathematical Communicator, Summer 1997, 1-8. Preprint: dvi-file or pdf-file Elliptic curves on abelian surfaces, Manuscripta Mathematica 84 (1994), 199-223. Preprint: dvi-file or pdf-file Idempotent relations among arithmetic invariants attached to number fields and algebraic varieties (with M. Rosen), J. Number Theory 46 (1994) 230-254. Discriminants of Hermitian R[G]-modules and Brauer's class number relation. In: Algebra and Number Theory - Proc. Conf. at IEM Essen, 1992 (G. Frey, J. Ritter, eds.) W. de Gruyter, Berlin, 1994, pp. 43-135. Preprint: dvi-file or pdf-file Curves of genus 2 covering elliptic curves and an arithmetical application (with G. Frey). In: Arithmetic Algebraic Geometry (G. van der Geer, F. Oort, J. Steenbrink, eds.), Progress in Math. 89, Birkhauser Boston, 1990, 153-176. Idempotent relations and factors of Jacobians (with M. Rosen), Math. Ann. 284 (1989) 307-327. Bounds on the number of non-rational subfields of a function field, Inventiones mathematicae 85 (1986) 185-198. Relations between the genera and between the Hasse-Witt invariants of Galois coverings of curves. Canad. Math. Bull. . 28 (1985) 321-327. On Castelnuovo's equivalence defect, J. reine angew. Math.. 352 (1984) 24-70. Selected Presentations -- see also the complete list The Hasse-Weil Zeta Function of a Quotient Variety CMS Conference Waterloo, Ontario , 4-6 June, 2005. Endomorphisms of Jacobians of Modular Curves and an Application CMS Conference, Montreal, Quebec, 11-13 December, 2004. Mazur's Question and Modular Diagonal Quotient Surfaces. Quebec-Maine Conference U Laval, Quebec , 2-3 October, 2004. Endomorphisms of Jacobians of Modular Curves 60th Birthday Conference of G. Frey, Essen, Germay , 7-10 July, 2004. The number of covers of an elliptic curve. AMS Conference Chapel Hill, North Carolina , 24-25 October, 2003. Hurwitz spaces of covers of elliptic curves. Quebec-Maine Conference U Laval, Quebec , 12-13 October, 2002. The class number relations of Kronecker, Gierster and Hurwitz. CMS Conference U Laval, Quebec , 15-17 June, 2002. Hurwitz spaces of genus 2 covers of elliptic curves. CMS Conference U Laval, Quebec , 15-17 June, 2002. Modular Diagonal Quotient Surfaces. Far Hills Workshop on Hilbert Modular Varieties. Far Hills Hotel (near Montreal), 3-6 January, 2002. Hurwitz spaces of genus 2 covers of elliptic curves. AMS Conference CA Irivine, California , 10-11 November, 2001. Equivariant Atkin-Lehner Theory. Mini Workshop on Arithmetic Geometry (G. Frey), Inst. Exp. Math., Univ. Essen, 4--6 June, 2000. The state of the art of elliptic curve cryptography. CITO Conference: Layers of Security CITO, Ottawa, 3 February, 2000. p -adic representations of the K -rational geometric fundamental group. Galois Actions and Geometry (P. Debes, H. Nakamura, A. Tamagawa), Math. Sci. Research Institute (MSRI), Berkeley, 11--15 October, 1999. Mazur's question for mod 11 Galois representations. Workshop on Algebraic Modular Forms and Modular Forms mod p (H. Darmon, M. Savin), CRM, University of Montreal, Montreal, 1--7 October, 1998. Mazur's question for mod 11 Galois representations. ICM-1998 Satellite Conference Algebraic and Arithmetic Geometry (H. Esnault, G. Frey, E. Viehweg), Universitaet Essen, 10--14 August, 1998. Diagonal quotient surfaces and a question of Mazur. Number Theory and Arithmetical Geometry: Arithmetical Applications of Modular Forms (G. Frey, J. Bost), San Feliu de Guixols, Spain, 24--29 October, 1997. Diagonal quotient surfaces and a question of Mazur. Algebraic Number Theory (C. Deninger, G. Frey, P. Schneider, A. Scholl), Oberwolfach, Germany, 20--26 July, 1997. {Tagungsbericht Oberwolfach 1997, p.\ }. Fermat's Last Theorem. (6 November 1996; Coleman-Ellis lecture, Queen's University, Kingston). Applications of diagonal quotient surfaces to a problem of Mazur. Conference on Arithmetic Algebraic Geometry (H. Koch, J. Kramer, E.-W. Zink), Berlin, Germany, 21--26 March, 1996. {Max-Planck Institute f\"ur Mathematik Bonn Preprint No.\ 1996-51, 5pp.} Diagonal quotient surfaces. Conference on Arithmetic Algebraic Geometry (H. Esnault, E. Viehweg, G. Frey), Institute for Experimental Mathematics, Essen, Germany, 21--24 November 1995. The Noether formula. Advanced Workshop on Arithmetic Algebraic Geometry II, Ain Shams University, Cairo, Egypt, 4--15 September 1993.} Curves of genus 2 with elliptic differentials and the Height Conjecture for elliptic curves. Conference on Finiteness Theorems in Number Theory (G. Frey), Essen, Germany, 12-15 March 1991. {Inst. Exp. Math. Essen, Preprint No. 18-1991, pp. 30-39}. See also Errata et Addenda. Recent Graduate Students C. Wan, Isomorphisms of Galois representation of elliptic curves over F_p, M.Sc.II (2004 Fall). S. Mohit, The zeta-function of modular diagonal quotient surfaces, Ph.D. (2002 Spring). A. VanTuyl, The field of N-torsion points of an elliptic curve over a finite field, M.Sc.II (1997 Fall). G. Wiesend, G-equivariant Riemann-Roch Theorems, M.Sc. (1995 Spring). A. Such, Endomorphisms of elliptic curves via p-divisible and formal groups. (1994 Spring). Undergraduate Student Research Projects T. Herland (4th year Math Engineering Project, 2003 2004): Digital Signatures. N. Alexander, J. Tytaneck (NSERC Summer Project, 2003): Cryptography: The Schoof-Elkies algorithm. - Errata for Schoof's 1985 paper by N. Alexander and J. Tytaneck M. Carmosini (NSERC Summer Project, 2000): Cryptography: The Schoof algorithm. A. Durward (4th year Math Engineering Project, 1999 2000): Techniques in Cryptography. D. Tie Ten Quee J. Wan (4th year Math Engineering Project, 1999 2000): Public Key Encryption Protocols. D. Stroszka (NSERC Summer Project, 1999): Finite field algorithms. P Williams (Summer Project, 1990): Algebraic structures. R. McCann (NSERC Summer Project, 1987): Plotting algebraic curves. Recent Graduate Courses Math 812: Elliptic curves and modular forms (Fall 2003) Math 918: Galois representations and modular diagonal quotient surfaces (Winter 2000) Math 918: Atkin-Lehner Theory and the Shimura construction (Fall 1999) Math 815: Number Theory and Cryptography (Fall 1999) Seminar on Modular Forms (Winter 99) Seminar on Hurwitz spaces (with S. Wevers) (Fall 98) Math 912: Rational points on elliptic curves (Fall 98) Math 811: Seminar on Galois Theory (with R. Murty) (Winter 98) Math 812: Modular Forms and L-functions (with R. Murty) (Winter 97) Math 917: Rational points on elliptic curves (Fall 94) Math 918: The Lefschetz-Riemann-Roch Theorem (Winter 94) Math 918: Curves of genus 2 with elliptic differentials (Winter 93) Seminar on modular elliptic curves (Fall 92) Relative Kurven [Relative curves] (University of Erlangen (Germany), Winter Semester 91 92) Seminar on codes, lattices and elliptic surfaces (Winter 91) A Personal Note My non-mathematical interests include white-water canoeing and wilderness camping canoeing, skiing and squash.
Klners, Jrgen
Universitt Kassel. Algebraic number theory, computational class field theory, Galois rheory, computer algebra. KANT software, tables of extensions of the rationals which contains polynomials for all Galois groups up to degree 15.
Jrgen Klners Jrgen Klners Fachbereich fr Mathematik und Informatik der Universitt Kassel Heinrich-Plett-Str. 40 34132 Kassel Germany E-Mail: klueners@mathematik.uni-kassel.de Telefon: +49 561 804-4192 Telefax: +49 561 804-4646 Fields of mathematical interest: Algebraic Number Theory, Computational Class Field Theory, Galois Theory, Computer Algebra I have developed and implemented algorithms for algebraic number fields. All algorithms are implemented in the computer algebra system KANT . Have a look at the homepage of our research group Computational Mathematics . I have created a database for field extensions of the rationals which contains polynomials for all Galois groups up to degree 15. Research Publications Lehre (in German) bungsbltter Diskrete Strukturen II Private stuff (Chess,...) (in German) Some useful links webmaster Last modified: Thu Oct 27 11:04:32 CEST 2005
Kisin, Mark
University of Chicago. p-adic Hodge theory and its applications; the p-adic Riemann-Hilbert Correspondence; p-adic modular forms.
Mark Kisin Mark Kisin's Webpage I work at the Mathematics Department at the University of Chicago Postal address: Dr Mark Kisin Department of Mathematics University of Chicago 5734 S. University Avenue Chicago, IL, 60637 Email: kisin[at]math[dot]uchicago[dot]edu Phone: +1 773 702 3064 FAX: Research Interests Here are some of my research interests and current projects You can find some of my papers here Teaching During Fall 2005 I am teaching Math 16100. Waterfall Me with food genius Tetsuya
Jimnez Calvo, Ismael
C.S.I.C., Madrid. Computational number theory. Papers, tables on Hall's conjecture.
Pgina de Ismael Jimnez Calvo Ismael Jimnez Calvo Pgina en espaol Personal details Born in Madrid, 11 11 1947. Tenured Scientist at the C.S.I.C., Madrid, Spain. Currently, I am working on Computational Number Theory. Curriculum vitae Some recent papers Hall's conjecture Quadratic residues Computer images Mountain photography Miscellany
Joyce, Adam
Imperial College, London. Modular forms, Manin constant. Preprints.
Welcome along Kezia Xena Adam Joyce Postgraduate, Room 677, Department of Mathematics , Imperial College , 180 Queens Gate, London, SW7 2AZ . Send me an email at: adam dot joyce at imperial dot ac dot uk I am a PhD student of Kevin Buzzard . Here's a picture of me with some of Kevin's other students. Papers "The Manin constant of an optimal quotient of J_0(431)", J. Number Theory, 110, (2005), no.2, pp325-330. .pdf , .dvi London Number Theory There is a very active London number theory group, meeting on Wednesdays. This term it meets at Imperial college, from 2pm in rm658. We are studying Deligne's conjectures on special values of L-functions. Go here to learn more. Go here to get Deligne's Corvallis paper.
James, Kevin
Clemson University. Fourier coefficients of modular forms and arithmetic applications. Publications, resources.
Kevin James Kevin James Assistant Professor Department of Mathematical Sciences Clemson University BOX 340975 Clemson, SC 29634-0975 Office: O-21 Martin Hall Phone: (864) 656-6766 (office) (864) 656-3434 (Dept) Fax: (864) 656-5230 Email: kevja@clemson.edu Schedule Spring 2005 Teaching: MthSc 119 (Discrete Math) : Tu,Th: 11:00 - 12:15pm in M-104 Martin Hall. MthSc 985 (Number Theory) : Tu,Th : 2:00-3:15pm in E-004 Martin Hall. Office Hours: Math 119: 11-12 W. Math 985: 11-12 M. Or email me to make an appointment. Research Interests Number theory. In particular, I am interested in the behavior of Fourier coefficients of modular forms and arithmetic applications. Departmental Seminars that I attend Informal Algebra and Number Theory Seminar. Algebra and Discrete Math Seminar Professional Information. Education Professional Experience Publications. Presentations of my research. Sponsored Research Honors and Awards Teaching Experience. College of Engineering Science CV Shorter CV Research Statement. download ps (1.5 MB) download dvi NO pictures (34K) Teaching Statement. view html download dvi Math Links REU in Computational Number Theory and Combinatorics. SERMON (South East Regional Meeting On Numbers). American Mathematical Society MathSciNet Algebraic Number Theory Archives Number Theory Web Other Math Departments on the web Last modified on 11 January 2005 Comments and questions to Kevin James (kevja@clemson.edu) .
Jacobson, Eliot
Unicersity of California, Santa Barbara. Algebraic, Elementary and Computational Number Theory. Teaching information, resources.
Home page for Eliot Jacobson, Ph.D. This page uses frames, but your browser doesn't support them.
Jarvis, Frazer
University of Sheffield. Algebraic number theory and algebraic geometry; in particular, the theory of modular forms and Galois representations. Publications, teaching materials.
Home page for Frazer Jarvis Frazer Jarvis's home page Contact details Department of Pure Mathematics, Hicks Building, University of Sheffield, Sheffield S3 7RH, Great Britain. Telephone: +44 114 2223845 Fax: +44 114 2223769 E-mail: a.f.jarvis@sheffield.ac.uk . Teaching I am a lecturer in the Department of Pure Mathematics at the University of Sheffield . In Autumn 2005, I shall be teaching PMA344 Real Analysis and PMA110 Numbers and Proofs . The links are to pages with copies of the notes, handouts, example sheets, past papers and solutions (when written!), which can be downloaded from within the University of Sheffield network. A selection of course notes for some of my previous courses, both graduate and undergraduate, are to be found here . Research My field of research is algebraic number theory and algebraic geometry; in particular, I am interested in the theory of modular forms and Galois representations. More details can be found on my main maths page , which also contains some references to my papers. This page is updated rather intermittently, but I hope to post more information on the page again soon. In particular, prospective research students will find a detailed description of my research interests. General information for prospective graduate students is available. Administration In Sheffield, I am the Pure Mathematics Level 1 Tutor. This involves allocating tutorial groups for several Level 1 courses . In addition, I can sign Level 1 Add-Drop Forms (in the first three weeks of any semester). If you need to see me, my office is J12 (or you can e-mail me ). I am also the secretary and Pure Mathematics representative on the Staff-Student Committee . I am also an Editorial Adviser for the London Mathematical Society . This involves advising the editors on papers submitted in the field of Algebraic Number Theory, for the three journals Proceedings of the London Mathematical Society , Journal of the London Mathematical Society , and Bulletin of the London Mathematical Society . To submit your manuscript to one of these journals, look at this page on the LMS web site . With Jayanta Manoharmayum , I organise the North of England Algebraic Number Theory Group , also known as NoMaDS, a group that meets several times a year in one of a the four universities Durham, Nottingham, Sheffield and Manchester. To be added to the mailing list, please e-mail me at a.f.jarvis@sheffield.ac.uk . Mathematical links Here are some mathematical societies and other useful sites: London Mathematical Society American Mathematical Society Socit Mathmatique de France EPSRC UK maths departments French maths departments German maths departments USA maths departments JSTOR Mathematics journals Number Theory web For an extensive list of preprint servers, click on the AMS list or the list at Penn State . For a list of electronic journals, click here . More mathematical links . Other interests In addition to mathematics, I am a keen pianist and musician. I sing with the Sheffield Philharmonic Chorus , and am one of the webmasters of their site. I collect classical CDs, mostly of piano music. Here is a discography of Marc-Andr Hamelin . More musical links may be found here. Other links , such as public transport timetables, and a few other useful things, are here. Searching the web Try Google advanced search . Frazer Jarvis, September 1st, 2005.
Janusz, Gerald J.
University of Illinois at Urbana-Champaign. epresentation theory of finite groups, algebraic number theory, Brauer groups, ring theory, algebraic coding theory. Selected publications, teaching material.
Gerald J. Janusz Gerald J. Janusz Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana, Illinois 61801-2975 Office: 375 Altgeld Hall Tel: (734) 944-1120 FAX: (217) 333-9576 e-mail: janusz@math.uiuc.edu General Information Ph.D. University of Oregon, 1965. Area of Specialization Representation theory of finite groups, algebraic number theory, Brauer groups, ring theory, algebraic coding theory. Selected Publications The Schur group of an algebraic number field, Annals of Math., 103(1976), 253-281. Automorphisms of simple algebras and group algebras, Proc. Philadelphia Conference, Dekker Lecture Notes, 37(1976), 381-388. Orthogonal groups of some trace forms, J. Pure and Applied Algebra, 29(1983) 297-312. Introduction to Modern Algebra, 6th Ed. Harcourt Academic Press, Burlington (2001) (text by N. McCoy, revised by G. Janusz) Permutation groups generated by a transposition and another element, L'Enseignement Math. 38 (1992), 41--53. Spreadsheets generate reservoir uncertainty distributions, Oil Gas Journal, (Mar. 13, 1995), 87--91. (with James Murtha) Hereditary Crossed Products, TAMS v.352 (2000) 3381-3410 with J. Haefner Overlap and Covering Polynomials with Applications to Designs and Self-dual Codes , SIAM J. on Discrete Math., v. 13, no.2, (2000) Overlap.dvi Maximal Designs--preprint design.dvi Construction of some self-dual binary codes (2002) SDCodes.dvi SDCodes.tex Parametrization of Self-Dual Binary Codes (Draft) 2004 Parametrization.dvi Parametrization.TEX
Jackson, Terence
University of York. Geometry of numbers, distribution of values of forms.
TERENCE JACKSON'S HOMEPAGE Terence Jackson E-mail: thj1@york.ac.uk Phone: 01904 43 3070, (+44) 1904 43 3070 (international) Research Interests: Since the 19th century a great deal of effort has been put into finding the lattice constants of bodies associated with quadratic forms. One outstanding case is the body 0 = x^2 -y^2 -z^2 -t^2 1. In 1931 Oppenheim found an admissable lattice for this body by looking at quaternary forms with large minima. However it is still not known if his lattice is critical. In the Acta Mathm et Inf. of Universitatis Ostraviensis (vol 10, pp43-48) I have used my recent isolation results about ternary forms of signature -1 to improve the known lower bound for the lattice constant in this case from 0.795.. to 0.918... Very recently J Bochnak and I have considered the distribution of small positive values of indefinite forms with at least 3 variables. Such a form is normalized when |d(f)| = 1 where d(f) is the determinant. Then, for each e 0, we have proved that a normalized indefinite f will represent a value v with 0 v e unless f is equivalent to one of a finite number of forms. This shows that, for indefinite forms in three or more variables, all the Markoff-type spectra are of discrete type. In recent years some new types of proofs have been found about the representation of primes by particular quadratic forms. The first of these was Heath-Brown's proof of Fermat's two-squares theorem in 1984. Then in 1990 Zagier gave a 'one-sentence' proof that required almost no background. I found a similar short proof of the fact that primes congruent to 3 modulo 8 are of the form x^2 + 2y^2 (Amer Math Monthly, vol 107, p447). My paper in the proceedings of the 1999 Turku conference gave a different short proof of this and also gave a direct proof that primes congruent to 7 modulo 12 are of the form x^2 + 3y^2 . In the proceedings of the 14th Czech Slovak number theory conference I have explored the connection between these direct proofs and automorphs of ternary quadratic forms. Return to Departmental Homepage
Jarden, Moshe
University of Tel Aviv, Israel. Field arithmetic. Contains articles, notes, and course information in postscript format.
Moshe Jarden's Home Page (TAU) Moshe Jarden School of Mathematics, Tel-Aviv University. Email: jarden@post.tau.ac.il Interest: Field Arithmetic Research (dvi format): Book: Field Arithmetic (2nd Edition): References Errata Articles: 43 : The absolute Galois group of a pseudo $p$-adically closed field (with D. Haran) 44 : On the normalizer of finitely generated subgroups of absolute Galois groups of uncountable Hilbertian fields of characteristic 0 (with W.-D. Geyer) 45 : On stable fields in positive characteristic (with W.-D. Geyer) 46 : The algebraic nature of the elementary theory of PRC fields 47 : Free pseudo $p$-adically closed fields of finite corank (with I. Efrat) 48 : Algebraic realization of $p$-adically projective groups 49 : The discriminant quotients formula for global fields, Appendix to Gopal Prasad's paper {``Finitenenss theorems for discrete subgroups of bounded covolume in semi-simple groups''} (with G. Prasad) 50 : The $p$-adic closure of a P$p$C field (with W.-D. Geyer) 51 : Skolem density problems over algebraic PAC fields over rings 52 : Compositum of Galois extensions of Hilbertian fieldS 53 : The Frattini subgroup of the absolute Galois group of a local field 54 : Hilbertian fields and free profinite groups 55 : Prosolvable subgroups of free products of profinite groups, 56 : Intersection of local algebraic extensions of a Hilbertian field 57 : Algebraic dimension over Frobenius fields, 58 : Effective counting of the points of definable sets over finite fields (with M. Fried and D. Haran) 59 : The inverse Galois problem over formal power series fields, 60 : Pseudo algebraically closed fields over rings (with A. Razon) 61 : On free profinite groups of uncountable rank, 62 : Rumely's local global principle for algebraic P$\calS$C fields over rings (with A. Razon) 63 : Large normal extensions of Hilbertian fields, 64 : Bounded Realization of l-groups over Global Fields (with D. Geyer) 65 : Regular split embedding problems over complete valued fields (with D. Haran) 66 : On Sigma-Hilbertian fields (with M. Fried) 67 : Regular split embedding problems over function fields of one variable over ample fields (with D. Haran) 68 : Random normal subgroups of free profinite groups (with A. Lubotzky) 69 : The projectivity of the fundamental group of an affine line, 70 : The absolute Galois group of $C(x)$ (with D. Haran) 71 : P$S$C Galois extensions of Hilbertian fields, (with W.-D. Geyer) 72 : Finiteness theorems for torsion of abelian varieties over large algebraic fields, (with M. Jacobson) 73 : Non PAC fields whose Henselian closures are separably closed, (with W.-D. Geyer) 74 : Skolem Density Problems for $\bbQgal[\sig_1,\dots,\sig_e]\cap\bbQ_{\tot,\calS}$ (with A. Razon), with an appendix by W.-D. Geyer 75 : Horizontal Isogeny Theorems (with G. Frey) 76 : On Ample fields, 77 : Torsion of abelian varieties over large algebraic fields (with Wulf-Dieter Geyer) 78 : Projective group structures as absolute Galois structures with block approximation (with Dan Haran and Florian Pop) 79 : Relatively projective groups as absolute Galois groups, (with D. Haran) 80 : P-adically projective groups as absolute Galois groups, (with D. Haran and F. Pop) 81 : A Karrass-Solitar theorem for profinite groups 82 : The rank of Abelian varieties over large algebraic fields, (with W.-D. Geyer) Notes: Stratification : Galois stratifiction for the elementary theory of finite fields p-adic : Elimination of quantifiers over $p$-adic fields and The rationality of the Poincar'e series of a variety over $Q_p$ FreeProduct : Free products of absolute Galois groups (with D. Haran and J. Koenigsmann) Skolem : Skolem fields, (with A. Razon) Courses: (in postscript format) Advanced Algebra I . Syllabus in Hebrew Table of Contents . Algebraic Functions 1 . Algebraic Functions 2 . Algebraic Functions 3 . Algebraic Functions 4 . Algebra B3 . Elliptic Curves . Syllabus in Hebrew Field Arithmetic Algebra B1 Exercises for Algebra B1 Mavo l'Algebra 2 Mordell Survey-elliptic School of Mathematics Algebra Dictionary Personal: Publication List Last update on 10.10.2005. Copyright M. Jarden and G. Cherlin Unique visitors since 5 October, 2005 Hits since 5 October, 2005
Jones, John
Arizona State University. Algebraic number theory: Iwasawa theory, the arithmetic of elliptic curves, Galois theory; questions in computational number theory. Tables of number fields of small degree. "Discovering number theory" course material.
John Jones Home Page John Jones Links Misc. Fun Pedagogy Courses MAT 443 MAT 543 Research Home Outside Links ASU Main ASU site Department of Mathematics and Statistics The Department of Mathematics and Statistics main site Contact Information Office: PSA 729 E-mail: Phone: (480) 965-3725 Fax: (480) 965-8119 Office hours: Monday 11:00-12:00, Wednesday 10:30-12:30, and by appointment. My history: a.k.a. my vita Last Update: September 19, 2005 Credits 2005 John Jones
Jutila, Matti
University of Turku. Analytic number theory. Publications.
Matti Jutila Matti Jutila Professor Office hours: Tuesdays 12-13 Postal address: Department of Mathematics University of Turku FI-20014 Turku, Finland Phone and Fax: +358 2 333 5606 +358 2 333 6595 (fax) E-mail: jutila@utu.fi Research interest: Analytic number theory Suomeksi Publications Curriculum Vitae | Mathematics | Personnel | | FacultyofMathematicsandNaturalSciences | | University of Turku |
Juricevic, Robert
University of Waterloo. Analytic number theory. Publications.
HomePage: Robert Juricevic Robert Juricevic Quebec City, Canada, February 2001 CONTACT RESUME ME, MYSELF, AND I
Jiang, Dihua
University of Minnesota. Automorphic Forms, Representation Theory, Number Theory.
dhjiang's Home Page Dihua Jiang Professor of Mathemtics School of Mathematics, University of Minnesota, 206 Church St. S.E., Minneapolis, MN 55455, USA. Office: 224 Vincent Hall, Phone No.: (612) 625-7532, Email: dhjiang@math.umn.edu Teaching Fall, 2005: Math 8300 (Topics in Algebra), Introduction to representations of p-adic groups. Notes will be distributed at class (course description) Fall, 2005: Math 4151 (Elementary Set Theory), Textbook "Elements of Set Theory" by Herbert B. Enderton. (Syllabus, Homework, and Exams) Math. Courses Taught in Previous Years (Math. Courses) Research Automorphic Forms, L-functions, Representation Theory, Number Theory research description ; recent work ; (math. review of my papers) ; math. people ; some photos Academic Experience (From 1989) Editorial Work Editorial Board (General Section) of The Journal of Algebra (2005--). Seminars and Conferences Lie Theory (Thursday) ; Automorphic Forms and Number Theory (Friday) Seminar Schedule, School of Mathematics Previous Conferences Recent Conferences: Automorphic Representations, L-functions and Applications: Progress and Prospects March 27--30, 2003, (Columbus) , Columbus, Ohio Arakelov Theory and Modular forms, NSF FRG Conference, University of Wisconsin at Madison, September 16-19, 2004. Automorphic Forms and Automorphic L-functions (RIMS) Jan. 17-21, 2005, Kyoto, Japan. Lie Groups and Automorphic Forms Summer School at The Center of Mathematical Sciences, Zhejiang University (CMS) July, 2005, Hangzhou, China, (announcement) Recent Trends in Endoscopy and Representation Theory Berlin Oct. 17-22, 2005, Berlin, Germany Math Links Morningside Center of Mathematics , Beijing, China Center of Mathematics Sciences , Hangzhou, China Arithmetc Geometry ; Number Theory ; Representation UCDavis-link ; e-preprint LiE K-preprints Interview with J.-P. Serre Other Links Travel Information Ph. D. Program Jokes Math Home Page
Jacobson, Michael
University of Manitoba. Computational aspects of quadratic orders. Papers and thesis.
Homepage of Michael Jacobson Michael J. Jacobson, Jr. Department of Computer Science University of Manitoba Winnipeg, Manitoba, Canada R3T 2N2 Phone: (204) 474 8995 Fax: (204) 474 7609 jacobs@cs.umanitoba.ca If you're not into computational number theory, you may want to make a quick escape to here . Topics of Current Research: My main area of research is computational aspects of quadratic orders. In particular, I am interested in computing the structure of ideal class groups and, in the case of real quadratic orders, the regulator, i.e., the natural logarithm of the fundamental unit. These problems are at least as difficult as factoring integers, and hence are also of interest in a cryptographic context. My doctoral work focused on an improvement of the sub-exponential algorithm for class group and regulator computation which results in significantly better practical performance. I have also used these new techniques to improve the algorithms for solving discrete logarithm problems in the class group and the infrastructure. My current work includes investigating cryptographic aspects of non-maximal real quadratic orders, searching for quadratic class groups with non-cyclic p-Sylow subgroups, and investigating the practical impact of these ideas on the subexponential algorithm for computing discrete logarithm in quadratic congruence function fields with high genus. Degrees: Dr. rer. nat. in Computer Science, Technische Universitt Darmstadt, 07 99 Subexponential Class Group Computation in Quadratic Orders, Technische Universitt Darmstadt, Darmstadt, Germany, 1999. Published by Shaker Verlag GmbH . ( ps abstract ) ( pdf abstract ) M.Sc. in Computer Science, University of Manitoba, 10 95 Computational Techniques in Quadratic Fields, University of Manitoba, Winnipeg, Manitoba, 1995. Postscript format: ( postscript ) ( gzipped ) PDF format: ( pdf file1 ) ( pdf file2 ) B.C.Sc. (Hon), University of Manitoba, 02 94 Publications: Towards practical non-interactive public-key cryptosystems using non-maximal imaginary quadratic orders. ( ps version) ( pdf version) To appear in Designs, Codes, and Cryptography , 2001. (with D. Hhnlein and D. Weber). Computational aspects of NUCOMP. ( ps version) ( pdf version) To appear in Algorithmic Number Theory - ANTS-V (Sydney, Australia), volume 2369 of LNCS, 2002. (with A.J van der Poorten). A computational approach for solving y^2 = 1^k + 2^k + ... + x^k. To appear in Math. Comp. , 2001. (with . Pintr, and P.G. Walsh). Modular arithmetic on elements of small norm in quadratic fields. To appear in Designs, Codes, and Cryptography , 2001. (with H.C. Williams). New quadratic polynomials with high densities of prime values. ( ps version) ( pdf version) To appear in Math. Comp. , 2000. (with H.C. Williams). Algorithms for large integer lattice problems. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - AAECC-14 (Melbourne, Australia), volume 2227 of LNCS, 2001, pp.297-307. (with M. Giesbrecht and A. Storjohann). Solving elliptic curve discrete logarithm problems using Weil descent. preprint Journal of the Ramanujan Mathematical Society , Vol. 16 (2001), no. 3, pp. 231-260. (with A.J. Menezes and A. Stein). The efficiency and security of a real quadratic field based key exchange protocol, ( ps version) ( pdf version) In Public-Key Cryptography and Computational Number Theory (Warsaw, Poland), de Gruyter, 2001, pp. 89-112 (with R. Scheidler, and H.C. Williams). Towards practical non-interactive public-key cryptosystems using non-maximal imaginary quadratic orders (extended abstract). ( ps version) ( pdf version) Seventh Annual Workshop on Selected Areas in Cryptography - SAC2000 (Waterloo, Canada), LNCS, vol. 2012, 2001, pp. 275-287. (with D. Hhnlein and D. Weber). The size of the fundamental solutions of consecutive Pell equations. ( ps version) ( pdf version). Experimental Mathematics , Vol. 9 (2000), no. 4, pp. 631-640. (with H.C. Williams). Computing Discrete Logarithms in Quadratic Orders. ( ps version) ( pdf version) Journal of Cryptology , Vol. 13 (2000), pp. 473-492. Analysis of the xedni calculus attack. ( ps version) ( pdf version). Designs, Codes, and Cryptography , Vol. 20 (2000), No. 1, pp.41-64. (with N. Koblitz, J.H. Silverman, A. Stein, and E. Teske). Applying sieving to the computation of quadratic class groups. ( ps version) ( pdf version). Math. Comp. , Vol. 68 (1999), No. 226, pp.859-867. Experimental results on class groups of real quadratic fields (extended abstract). ( ps version) ( pdf version). In Algorithmic Number Theory - ANTSIII (Portland, Oregon), volume 1423 of LNCS, 1998, pp.463-474. A cryptosystem based on non-maximal imaginary quadratic orders with fast decryption. ( ps version) ( pdf version). In Advances in Cryptology - EUROCRYPT '98, volume 1403 of LNCS, 1998, pp.294-307. (with D. Hhnlein, S. Paulus, and T. Takagi). Sieving methods for class group computation. ( ps version) ( pdf version). In Proceedings of Algorithmic Algebra and Number Theory, Heidelberg, 1998. Springer (with J. Buchmann, S. Neis, P. Theobald, and D. Weber). On some computational problems in finite abelian groups. ( ps version) ( pdf version). Math. Comp. , Vol. 66 (1997), No. 220, pp.1663-1687 (with J. Buchmann and E. Teske). An Investigation of Bounds for the Regulator of Quadratic Fields. ( ps version) ( pdf version). Experimental Mathematics , Vol. 4 (1995), No. 3, pp.211-225 (with R.F. Lukes and H.C. Williams). CompSci Homepage Owner of this page: Michael Jacobson -- jacobs@cs.umanitoba.ca UofM CompSci WWW Administrator -- www@cs.umanitoba.ca UofM Campus WWW Administrator -- www@umanitoba.ca
Jimnez, Enrique Gonzlez
University of Nottingham. Modular hyperelliptic curves, Q-curves, modular Abelian varieties. Tables of modular curves.
Enrique Gonzlez Jimnez Enrique Gonzlez Jimnez Research Number Theory: Modular Hyperelliptic Curves, Q-curves, Modular Abelian Varieties. Publications "Modular Hyperelliptic Curves" Ph.D.thesis (in Spanish), January 2002. Abstract: English , Spanish . "Modular Curves of Genus 2" with Josep Gonzlez. Math. Comp. 72 (2003), no. 241, 397-418. Preprint version: pdf . "Computations on Modular Jacobians Surfaces" with Josep Gonzlez and Jordi Gurdia, Algorithmic number theory (Sydney, 2002), 189--197, LNCS 2369, Springer, Berlin, 2002. Preprint version: pdf . "Finiteness Results for Modular Curves of Genus at Least 2", with Matthew Baker, Josep Gonzlez and Bjorn Poonen. Preprint version: pdf . Tables New Modular Hyperelliptic Curves . Genus 2 curves with modular jacobians . Modular Q-curves . School of Mathematical Sciences University of Nottingham University Park Nottingham, NG7 2RD, UK Phone: (+44)-(0)115-9514984 Fax: (+44)-(0)115-9514951 Email: enrique.gonzalez@nottingham.ac.uk Created: March 15, 2001. Last modified: November 26, 2002. http: www.maths.nottingham.ac.uk personal pmzeg1
Jochnowitz, Naomi
University of Rochester. Algebraic number theory, modular forms, p-adic modular forms.
UR Department of Mathematics - Naomi Jochnowitz Naomi Jochnowitz Department of Mathematics University of Rochester Rochester, NY 14627 Office: Hylan 1003 Fax: (716) 244-6631 E-mail: what@math.rochester.edu Research Interests Algebraic number theory, modular forms, p-adic modular forms.
Ishii, Noburo
Osaka Prefecture University. Algebraic Number Theory, especially automorphic forms of one variable, elliptic and modular curves; Cryptography. Publications.
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Iovita, Adrian
University of Washington, Seattle. Local Galois representations attached to modular forms and global applications; p-Adic L-functions; p-Adic families of Galois representations. Publications.
Adrian Iovita's webpage at the University of Washington
Imamoglu, Ozlem
University of California, Santa Barbara. Automorphic forms. Contact information.
Ozlem Imamoglu Web Site (none) Contact Information Office: South Hall 6708 Phone: (805) 893-8309 Fax: (805) 893-2385 Email: ozlem@math.ucsb.edu Area of Research Number Theory, Automorphic Forms
Im, Bo-Hae
Indiana University. Mordell-Weil groups and the rank of elliptic curves over large fields.
home.html BO-HAE IM Bo-Hae Im's homepage has been moved to http: www.math.utah.edu ~im .
Huang Sen-Shang
National Changhua University of Education. Analytic number theory.
Sen-Shang Huang's Homepage ( Sen -Shan Huang) Associate Professor Department of Mathematics National Changhua University of Education Changhua 500, TAIWAN Office: 21206 Office Tel: (04) 7232105 ext. 3243 E-mail: sshuang@cc.ncue.edu.tw ; shuang@math.ncue.edu.tw Education Ph.D. University of Illinois at Urbana-Champaign Advisor Bruce C. Berndt Courses (given in Fall , 2005) Algebra I Analytic Number Theory I Prpblem Solving in Mathematics I Research Interest Analytic number theory Publications and Research Projects
Holdener, Judy
Kenyon College. Odd perfect numbers; theoretical morphology. Teaching technology, GAP projects.
Judy Holdener's Homepage Judy A. Holdener Associate Professor of Mathematics email: holdenerj@kenyon.edu Department of Mathematics, Kenyon College, Gambier, OH 43022 office phone: 740-427-5266 About Me: Contact Information Vita Research with Undergraduates Art Personal Photos Current Courses: Math 213: Multivariable Calculus Math 327: Number Theory Seminar Teaching: Office Hours (Fall, 2005) Course Archives (2001-2004) Calculus Projects Abstract Algebra Projects Teaching Photos Other: Useful Links Some good quotes... "Abundancy" by Judy Holdener acrylics on canvas, 36'' x 36'' This painting was created with the help of mathematics! Read more about this... The views and opinions expressed in this page are strictly those of its information provider. The provider assumes full responsibility and liability for the content of this document. The contents of this page have neither been reviewed nor approved by Kenyon College. All comments and feedback should be sent to holdenerj@kenyon.edu . Back to the Kenyon Homepage Back to the Math Homepage Last Modified: August 21, 2005
Hahn, Heekyoung
University of Rochester. q-series, continued fraction, theta functions, partitions, modular forms, Eisenstein series, special functions; elliptic curves, coding theory and the philosophy of mathematics. List of publications.
Heekyoung Hahn's Home Page Site map Search : University of Rochester Mathematics Home People Faculty hahn Heekyoung Hahn Assistant Professor Department of Mathematics University of Rochester Rochester, NY 14627 Office: Hylan 805 Phone: (585) 275-9418 Fax: (585) 273-4655 E-mail: hahn@math.rochester.edu General Information In 2004, I received my Ph.D. from the Department of Mathematics at the University of Illinois at Urbana-Champaign under supervision of my advisor Bruce Berndt . Teaching Fall 2005 MTH230: Theory of numbers Spring 2005 MTH161: Calculus IA MTH165: Linear Algebra with Differential Eq. Fall 2004 MTH142: Calculus II MTH164: Multidimensional Calculus Research Interests My primary interests are q-series, theta functions, partitions, modular forms, Eisenstein series, L-functions, Riemann zeta function, Dirichlet polynomials, but I am also quite fond of elliptic curves, coding theory and the philosophy of mathematics. Publications New Ramanujan-Kolberg type partition identities (with H. H. Chan, R. P. Lewis, and S. L. Tan), Math. Res. Lett. 9 (2002), no. 5-6, 801-811. Septic analogues of the Rogers-Ramanujan functions, Acta Arith. 110 (2003), no. 4, 381-399. Eisenstein series associated with Gamma_0(2), submitted. Convolution sums of some functions on divisors, Rocky Mt. J. Math., to appear. Ramanujan's forty identities for the Rogers-Ramanujan functions (with B. C. Berndt, G. Choi, Y. Choi, B. Yeap, A. J. Yee, H. Yesilyurt, and J. Yi), submitted. MathSciNet listings for Heekyoung Hahn Conferences AMS Special Session, `Special functions, orthogonal polynomials, and their applications', Evanston, Illinois, October 23-24, 2004. Additive Number Theory, University of Florida. November 17-20, 2004. Last modified: Tuesday, 18-Aug-2004 18:09:48 EDT Send feedback about this page 2004 UR Mathematics Check XHTML The URL for this document is http: www.math.rochester.edu people faculty hahn Navigation Home Announcements About Courses People Faculty Hahn ... Graduate students Staff Research groups Graduate Undergraduate
Helfgott, Harald A.
Universit de Montral. Number theory, elliptic curves, automorphic forms, combinatorics. Publications, teaching materials.
H. A. Helfgott Harald Helfgott Basic data on HH Publications and preprints Course materials Curriculum vitae: ps pdf Various Thanks
Hart, William
Leiden University. Special Values of Dedekind's Eta Function, Elliptic Units and Generalizations for Abelian Varieties, Stark Conjectures, Elliptic Functions, Modular Equations. Publications, notes, thesis.
Homepage of William Hart Dr. William Hart Postdoc at Leiden University Ph: + 33 (0)71 527 7149 Email: wbhart@SPAM.INVALID.math.leidenuniv.nl (Remove `SPAM.INVALID' to send mail) My CV is here. My research report is here. Research Interests: Special Values of Dedekind's Eta Function, Elliptic Units, Iwasawa Theory, The Stark Conjectures, Algebraic Number Theory, Elliptic Functions, Modular Equations, Algebraic K-theory. General Interests: I enjoy occasional bushwalking and exercise, computer programming (assembly language, C++, OpenGL), Bible study, electronics, astronomy (12" Newtonian reflector) and reading about other areas of science. Publications: Modular Equations and Eta Evaluations - Aust. Math. Soc. Gazette, Vol. 31 No. 1, Mar 2004, pp. 43--47 Evaluation of the Dedekind Eta Function - with Robin Chapman (to appear in the Canadian Mathematical Bulletin) Preprints: Schlaefli Modular Equations for Generalized Weber Functions (Submitted) Eta Evaluations from Modular Equations for Weber Functions Recent Work: I recently found a new kind of modular equation!! Similar to Weber's modular equations of `irrational kind', these equations are supremely useful in providing evaluations of class invariants. The above preprint "Eta Evaluations from Modular Equations for Weber Functions" is as a result, in the process of being dramatically expanded in scope (yes, there is a `method' now, working in an infinite number of cases). A further preprint on the somewhat elegant theory behind these new modular equations will also be added shortly. Work in Progress Planned Work: A look at whether Sharifi's work on bounding various Milnor $K$-groups of rings of certain $S$-integers associated with cyclotomic fields can be extended to the situation of unramified abelian extensions of imaginary quadratic fields. Shimura essentially gives, in his papers, a Shimura reciprocity law for Hilbert modular forms. This has not been made explicit. I plan to decipher Shimura's papers and work with Peter Stevenhagen to attempt to make this explicit. Doing some computations for Daniel Delbourgo who has some `crazy notions' of Euler products for $p$-adic $L$-series, which don't seem that crazy. PhD Thesis (Macquarie University Sydney): Evaluation of the Dedekind Eta Function Other Typed Material: Algebraic Number Theory - The Basics Algebraic Number Theory - The Algebraic Method Slides on Modular Equations of Higher Signature Notes on Functions of a Complex Variable - Currently Being Edited A Guide to Theta Functions and Weber's Modular Equations Notes on Cohomology (following MacLane's "Homology") - Not Yet Fully Complete Notes on the GL_2 Main Conjecture a la Coates, Fukaya, Kato, Sujatha and Venjakob Links: Other People's Lecture Notes on Mathematical Topics Photos: Photos in Besanon
Hare, Kevin G.
University of Waterloo. Algebraic numbers, polynomials. Publications, worksheets.
Kevin Hare's Home Page Contact Info Kevin Hare Phone: (519) 885 1211 X 5556 MC 5086, Department of Pure Mathematics The University of Waterloo Waterloo Ontario Canada Current Courses PMath 352 (Complex Analysis), Fall 2005 PMath 370 (Chaos and Fractals), Fall 2005 Other Useful Stuff Preprints A Picture I happen to like This is related to the roots of +1, -1 polynomials. Computational Mathematics Centre at Waterloo
Helenius, Ola
Goteborg University. Picard groups for integer group rings. Theses, preprints.
Ola Helenius Ola Helenius
Harman, Glyn
Royal Holloway University of London. Analytic number theory: application of sieve methods, Diophantine approximation, metric number theory.
Glyn Harman's Home Page Professor Glyn Harman B.Sc.,Ph.D.(London),D.Sc.(Wales) Research Interests Most areas of analytic number theory. In particular: application of sieve methods, Diophantine approximation, metric number theory. E-mail address : g.harman@rhul.ac.uk Date of birth : 2nd November 1956 Member of the London Mathematical Society, twice a recipient of a distinguished award of the Hardy-Ramanujan Society for his work with R.C.Baker and J. Pintz on primes in short intervals. Family information : Son of the Welsh poet Raymond Harman (an anthology of his work entitled "A Resounding Voice and Echoes of the Welsh Valleys" is published by Horseshoe Publications ISBN 1 899310 22 3). Married to Ruth (occupational therapist) with children Matthew, Jonathan and Christopher. Outside interests : music; formerly one of the elders and trustees of Thornhill Church Cardiff , now worships at Barkham Church , Member of the Victoria Institute (also known as "Faith and Thought").
Hajir, Farshid
California State University, San Marcos. Elliptic curves, extensions with restriced ramification, and special values of L-functions. On-line seminar, teaching information.
Farshid Hajir Farshid Hajir's Home Page Farshid Hajir Assistant Professor of Mathematics California State University, San Marcos San Marcos CA 92096 phone: 760-750-8031, fax: 760-750-????, e-mail: fhajir@csusm.edu Online Seminar: Galois theory of p-extensions Course information (Spring 2001) Math 522: Number Theory Research Interests My main area of study is Number Theory: I am particularly interested in elliptic curves, extensions with restriced ramification, and special values of L-functions. Preprints, curriculum vitae, and other information, such as a description of my research, coming soon . Some math web pages A mathematician is a machine for turning coffee into theorems. -- Paul Erdos (1913-1996) Departmental Home Page of the CSUSM Math Department. AMS Home Page The American Mathematical Society. Number Theory Web Many links concerning one of the oldest branches of mathematics. Algebraic Number Theory Archives: Some (p)reprints in algebraic number theory. MacTutor History of Mathematics archive UCLA Math Department Soccer! Soccer! Soccer! SoccerAmerica. Frequently updated soccer news and information. Major League Soccer. LA Galaxy, SJ Clash, DC United, and the other 7 teams. FIFA. The world governing body of soccer. Some other web sites CSUSM Home Page . Macintosh Archive. Contains stuff for the Macintosh. WebMuseum, Paris. An online museum of art. USA Today. Good source of soccer news, especially NCAA. You may reach me via e-mail at fhajir@csusm.edu
Hess, Florian
Technische Universitt Berlin. Algebraic function fields, algebraic number fields and algorithms.
Florian He Florian He Address: Prof. Dr. Florian He Technische Universitt Berlin Fakultt II Institut fr Mathematik Sekr. MA 8-1 Strae des 17. Juni 136 D-10623 Berlin Germany phone: +49-30-314-25062 phone: +49-30-314-24015 (secretary) fax : +49-30-314-21604 email: hess at math.tu-berlin.de Mathematics building, office MA804 Research Interests: Algebraic function fields, algebraic number fields and algorithms Applications of the above in cryptography and elsewhere Contents of this Webpage: Theses, Papers and Preprints Programs Courses ( Algebra 1 , Algebra 2 , Kryptographie 1 , Kryptographie 2 , Seminar ) Slides ( Introductory Magma talk slides and examples, IHP Paris 2004 ) Pictures ( Dagstuhl 2004 , ANTS VI ) Special events in number theory and cryptography at the TU Berlin: Number Theory Conference on the occasion of M. Pohst's 60th birthday, June 9 to 11 2005. KryptoLabor zur Langen Nacht der Wissenschaften am 11. Juni 2005: Wir sind bei der Langen Nacht der Wissenschaften 2005 mit dem KryptoLabor dabei. Allgemeine Informationen zur Langen Nacht finden sich hier . Algorithmic Number Theory Symposium VII, July 23 to 28, 2006. KANT Project | Mathematics Department | TU-Berlin | IACR | Google Last modified: Mon Aug 29 2005
Hughes, Chris
University of Michigan. Application of random matrix theory to the Riemann zeta function and other L-functions. Publications, resources.
Chris Hughes homepage Chris Hughes' homepage My stuff: Papers Links Zeta poem AIM: AIM Home Page About me I am an Assistant Professor in Department of Mathematics at the University of Michigan. My research involves studying how one can apply random matrix theory to the Riemann Zeta function and other L-functions. I can be contacted at Department of Mathematics University of Michigan 530 Church Street Ann Arbor, MI 48109-1043 USA Tel: (734) 936-4051 Email: hughes @ aimath.org Office: 1832 East Hall I visited the Isaac Newton Institute for Mathematical Sciences for the six months of 2004, attending the programme on Random Matrix Approaches in Number Theory . Previously, in 2002-2003, I was a postdoc at the American Institute of Mathematics , and in 2001-2002 I was a postdoc in the School of Mathematical Sciences at Tel Aviv University , where I was funded by EC Network Mathematical Aspects of Quantum Chaos . Before that, I did my PhD in the mathematics department of the University of Bristol , where my work was sponsored by BRIMS , at Hewlett-Packard Laboratories Bristol . My cv . Links to other pages at this site The links page: many web sites connected to the Riemann zeta function, and its generalizations. A poem about the Riemann Zeta Function, which I found on the web, but can't remember where! A list of my papers .
Howson, Susan
University of Oxford. Arithmetic of elliptic curves, Iwasawa theory, p-adic L-functions and the theory of Euler systems. Papers, seminars and other resources.
Susan Howson
Garthwaite, Sharon Anne
University of Wisconsin - Madison. Modular forms, partitions. Education, outreach.
Sharon Anne Garthwaite University of Wisconsin, Madison Mathematics Department 480 Lincoln Drive Madison, WI 53706 How to Find Me: email id: garthwai (preferred) phone: (608) 294-5626 office: 416 Van Vleck Greetings! I am a 3rd year grad student here at UW. My advisor is Prof. Ken Ono. My Mathematical Interests include Number Theory Modular Forms Partitions Math Education (I am currently working towards a minor in Mathematics Education through the Curriculum Instruction Dept.) How I spend my Time: Teaching Non-Mathematical Interests Outreach Program for High School Women : a program for high school girls interested in math College For Kids : A summer program held at UW Madison for talented youth in the Madison area who are entering the sixth grade in the Fall. Nathan Panike and I taught a workshop on Probability during Summer 2005. Curriculum Vitae Publication : Convolution Congruences for the Partition Function, accepted for publication in Proceedings of the American Mathematical Society Guide For Incoming UW Math Grad Students
Goins, Edray Herber
Purdue University. Arithmetic of elliptic curves; Galois representations. Publications, outreach.
Edray Herber Goins
Goss, David
Ohio State University. Zeta-functions, gamma functions, motives, Drinfeld modules, modular forms, Galois representations, special-values, non-archimedean analysis, K-theory. Publications, books.
David Goss' Personal Homepage David Goss This home page contains information that I believe will be of interest to mathematicians, in general, and number theorists, in particular. It contains links to various preprints, papers, and books that I have written or edited. (In particular, there is a sample chapter from, my book "Basic Structures of Function Field Arithmetic," [ cover.jpg ] which was published on October 17, 1996 as well as information on the soft-covered "study" edition published on November 18, 1997.) Finally it contains a link to files on mathematical writing. It should be considered as being in perpetual construction. For information on Math 151A go here. Quite recently, Gebhard Boeckle, wrote an ETH habilitation thesis in which he used the theory of "crystals" for function fields to associate Galois representations to Hecke cuspidal and double cuspidal eigenforms in finite characteristic. (A copy of this thesis is available the site linked to Boeckle below.) This is major breakthrough in the characteristic p theory. It is also a complex work which uses almost all the machinery invented so far! Boeckle's Galois representations are abelian (in contrast to what happens classically, although even classical Dirichlet characters arise from modular forms of fractional weight). In the simplest case where our base algebra is the ring of polynomials over a finite field, it then makes sense to ask if rank 1 Drinfeld modules can be modular in that their associated Galois representations arise from modular forms. In a preprint, (what follows is the final, edited, version) here.dvi , here.pdf , here.ps , we present an introduction to Boeckle's work with an emphasis on modularity in both the classical (elliptic curves over Q AND over a function field) and characteristic p theories. This preprint is published in the Journal of the Ramanujan Math. Soc. {\bf 17} No. 4 (2002) 221-260. In Mathematische Annalen 323 (2002) 737-795, Gebhard Boeckle shows how to analytically continue the L-series associated to "tau-sheaves." Such sheaves arise naturally from Drinfeld modules as well as general A-modules (in the sense of G. Anderson) and have become the basic structure of characteristic p arithmetic. Boeckle's proof uses essentially the logarithmic growth of the degrees of the "special polynomials" associated to these L-series. In a new paper, we show how to use non-Archimedean integration to analytically continue such L-series as well as ALL associated partial $L$-series. Our proof uses the logarithmic growth and certain deep estimates of Amice. An interesting point of the proof is the way that the analytic theory of L-series at all(!) places of base field k is needed to establish the result. (Final version put online May 3, 2004 -- to appear in the Journal of Number Theory.) For a copy, go here.dvi, here.ps, or here.pdf. In a 1999 preprint we explained how to formulate the characteristic p "Generalized Riemann Hypothesis," as well as the characteristic p version of the "Generalized Simplicity Conjecture," in terms of absolute values. A corresponding reformulation of the classical statements is also given. The similarities between the "absolute value conjectures" in the two theories (i.e., classical and characteristic p arithmetic) are very strong and quite surprising. (See also the next two paragraphs.) For a copy of this preprint, go here.dvi , here.ps , or here.pdf . The published version of this paper is Journal of Number Theory vol. 82, no.2 (June, 2000) 299-322. The on-line version can be accessed at here . (See below for a site dedicated to current papers on the Riemann Hypothesis.) The Riemann Hypothesis in characteristic p is based on the work of D.Wan, D.Thakur and J.Diaz-Vargas, B.Poonen, and J.Sheats (exact references given in the above files) for the zeta function of F_r[T]. The zeta function is defined for (x,y) in S_\infty where x lies in a finite characteristic complete field and y is a p-adic integer. Thus one has a 1-parameter family of power series and an associated 1-parameter family of Newton polygons. One can therefore say more precisely that Wan, Diaz-Vargas, etc., compute the family of Newton polygons associated to this zeta-function. This family turns out to have segments with horizontal length identically 1, which establishes that the zeroes are both simple (i.e., of order 1) and in Fr((1 T)). In seeking to phrase this ``Rh'' for as large a class of characteristic p functions as possible, it was realized that one would have to allow for finitely many anomalous zeroes for each y. Now for y a negative integer one only has finitely many trivial zeroes; thus we simply ignored these trivial zeroes (and so the infinite primes) in formulating these conjectures. Since the publication of the above manuscript, it was realized that this assumption is in error; that is, the trivial zeroes, and so the infinite primes, must be taken into account. What happens is that the topology on S_\infty allows us to use zeroes close to trivial zeroes (``near-trivial zeroes'') to inductively construct counter-examples. This is contained in ``The impact of the infinite primes on the Riemann hypothesis for characteristic p valued L-series,'' which appears in the book "Algebra, Arithmetic and Geometry with Applications", (Eds: Christensen et al) Springer (2004) 357-380. For the preprint see here.dvi , here.ps or here.pdf ,. In this paper we also begin to come to grips with the implications of these counter-examples. We explain how trivial and near-trivial zeroes should arise in general, and how they might ultimately be handled via Hensel's Lemma (whereas classically one uses Gamma-functions). We break up all the zeroes into two classes, the near-trivial zeroes and the ``critical zeroes'' (= all other zeroes). But then there is a remarkable surprise: All zeroes computed by Wan et al are near-trivial (this is established when r=p and should be true in general). Thus, while it is reasonable to believe that these critical zeroes will exist in abundance, up to now we have had very little experience with them. Follow this link style for files on mathematical writing. The publisher for the "Basic Structures" volume is Springer and the Springer series which contains the book is Ergebnisse der Mathematik und ihrer Grenzgebiete, Vol. 35. Abstract for volume 35: The arithmetic of function fields over finite fields has been an area of extensive research for about two decades with many tantalizing results having recently been obtained. This book offers a self-contained introduction to basic concepts such as Drinfeld modules, T-modules, shtukas, exponentiation of ideals, and characteristic p L-functions and Gamma-functions in all their various manifestations. Insight from classical number theory, differential equations algebra and algebraic geometry is presented whenever needed. Interesting unsolved problems are posed to the reader and a comprehensive list of references is included. All of this is presented to give the reader the basic tools to begin doing active research into this rapidly expanding area. The volume is ISBN 3-540-61087-1 and contains 415 references. Below is the .dvi file of the table of contents. Table of Contents of Vol. 35 Follow this link Springer Germany for the homepage of Volume 35 on www.Springer.de. Follow this link Springer New York for the homepage of Volume 35 on www.Springer-ny.com. The soft-covered study edition is priced at $59.95 and DM 108,- . It has 453 references and some minor corrections have been made. The ISBN number is 3-540-63541-6. In conjunction with Springer, I am very happy to be able to offer both a list of these corrections as well as the expanded references below. In addition, still in conjunction with Springer, I am delighted to offer the .dvi, .ps, and .pdf files of Section 3 "The Carlitz Module" as a sample of the book. For the .dvi file of Section Three. For the .ps file of Section Three. For the .pdf file of Section Three. For the .dvi file of the references. For the .ps file of the references. For the .pdf file of the references. For the list of corrections. In June, 1991, there was a conference at Ohio State on the arithmetic of function fields related to Drinfeld modules. The proceedings were published by de Gruyter in 1992 as "The Arithmetic of Function Fields," which is the second volume of de Gruyter's Ohio State University Mathematical Research Institute Publications. It was edited by D. Goss, D.R. Hayes and M.I. Rosen and is ISBN 3-11-013171-4. Below is the .dvi file of the table of contents of these proceedings. Table of Contents of Proceedings To find out more about this volume from de Gruyter, follow the next link and do a search under "Ohio" in the series box. de Gruyter The following are links to preprints of some other mathematicians interested in the arithmetic of function fields. If you know of other links that perhaps should be added to this list, please contact me at the address given below. Greg Anderson Gebhard Boeckle Gunther Cornelissen Henri Darmon Ernst-Ulrich Gekeler and his school Dinesh Thakur Doug Ulmer For a general list of number theorists, go here . For general list of number theory preprints, go here or here . For a collection of current papers about the Riemann Hypothesis go here . The address of the Department of Mathematics at The Ohio State University is 100 Mathematics Building, 231 W. 18-th Avenue, Columbus Ohio 43210-1174. I can be reached by email at goss@math.ohio-state.edu , by phone at 614-292-0869, and by fax at 614-292-1479. All correspondence concerning the Journal of Number Theory should be sent to jnt@math.ohio-state.edu . This page has been accessed 27499 times. Last modified Tue Sep 20 22:13:04 EDT 2005
Green, Ben J.
University of Bristol. Arithmetic combinatorics. Papers, preprints.
Ben Green This is Ben Green's website Outdoor Cricket Jazz Friends Maths Miscellany Click on a link for details
Gonek, Steve
University of Rochester. Analytic number theory, especially multiplicative number theory and the theory of the Riemann zeta-function. Publications.
UR Department of Mathematics - Steve Gonek Steve Gonek, Professor Department of Mathematics University of Rochester Rochester, NY 14627 Office: Hylan 1020 Phone: (585) 275-3419 Fax: (585) 273-4655 E-mail: gonek@math.rochester.edu Biographical Sketch and Research Interests Recent Publications Curriculum Vita Algebra Number Theory Seminar
Gal Istvn
University of Debrecen. Constructive methods for the complete resolution of Diophantine equations: Thue, norm form discriminant form, index form; Power integral bases in algebraic number fields. Publications, results, algorithms and tables of numerical data.
Istvn Gal Istvn Gal professor PhD, CsC, Habil, DsC head of Department of Algebra and Number Theory vice chair of School of Independent Faculties University of Debrecen Faculty of Science Institute of Mathematics H-4010 Debrecen, Pf.12 Hungary office: M220 telephone: -36-52-512900 ext.2802 fax:-36-52-416857 e-mail: igaal@math.klte.hu
Gee, Toby
Imperial College, London. Arithmetic of modular forms. Preprints.
Toby Gee Personal details Dr Toby Gee Picture Position: Research associate at Imperial College , London. Office: 682, Huxley Building. Extension: 58608 Postal Address: Department of Mathematics, Imperial College, 180 Queen's Gate, London SW7 2AZ, UK. Email: toby dot gee at imperial dot ac dot uk. My CV is here: dvi ps pdf Publications preprints "Companion forms over totally real fields", submitted dvi ps pdf "Companion forms over totally real fields, II" dvi pdf
Gerth, Frank E, III
University of Texas. Algebraic number theory, including class numbers, class groups, discriminants, class field theory, density theorems, Iwasawa theory. Contact information.
UT - Department of Mathematics - faculty members Gerth, Frank E, III, Ph.D., Princeton, 1972 Mathematics: Algebraic Number Theory. Professor. Phone: 471-1187 Office: RLM 12.162 Office hours: M 10:30-11:30 a.m., WF 12:45-1:30 (second session). gerth@math.utexas.edu
Ghate, Eknath
Tata Institute of Fundamental Research. Automorphic forms, Galois representations, and special values of L-functions. Publications, thesis, lecture notes.
Eknath Ghate's Home Page Eknath Ghate's Home Page Reader School of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road Mumbai, 400 005, India E-mail: eghate@math.tifr.res.in Phone: 91-22-2278-2663 (o) Phone: 91-22-2280-4545 ext. 2663 (o) Phone: 91-22-2280-4562 (h) I work in number theory, and am mostly interested in problems connected to automorphic forms, Galois representations, and the special values of L-functions. Math Mountains During the Fall sememster 2005, I'll be Visiting Associate Professor at Cornell University .
Galbraith, Steven
Royal Holloway University of London. Number theory, elliptic curves. Publications, thesis, resources.
Steven Galbraith Steven Galbraith Reader Mathematics Department Royal Holloway University of London Egham, Surrey TW20 0EX, UK. Email: Steven.Galbraith@rhul.ac.uk Room: 346 Tel: +44 1784 414396 Fax: +44 1784 430766 Upcoming events: Tenth IMA conference on cryptography and coding, Cirencester December 19-21, 2005. Asian Symposium on Computer Mathematics (ASCM 2005) , December 19-21, 2005. Spring school on abelian varieties , May 2-24, 2006. ANTS VII , July 23-28, 2006. Fields institute Thematic Program in Cryptography , Autumn 2006. Administrative duties: Maths department coordinator for exchange study abroad students. Course director for Masters degree MSc in Mathematics of Cryptography and Communications . Maths department ESO network member (support for students with special needs). Involved in outreach activities such as organising talks and workshops for 6th formers. Programme committees: Programme committee member ISC 2003. Programme committee member CT-RSA 2005. Programme committee member EUROCRYPT 2005. Programme committee member Codes and Cryptography, Cirencester 2005. Programme committee member WEWoRC (Leuven) 2005. Programme committee member CT-RSA 2006 . Member of Designs Codes and Cryptography editorial board. Notice: If you sent an email to me which has been rejected by my spam filter then please re-send to stepchook@hotmail.com (be warned that this account is not checked regularly). Number Theory Group Information Security Group Publications and preprints Thesis ECC Teaching Students SECANTS One day workshop in cryptographic number theory (2003) Mathematics Conference pictures Scotland holiday Personal Last Modified: 25-10-2005
Ghitza, Alexandru
CICMA and McGill University. Arithmetic geometry: the relation between modular forms and Galois representations. Thesis, preprints, talks.
Alex Ghitza's Page Alexandru Ghitza Office: McGill: Burnside Hall 1125 (805 Sherbrooke W), phone (514) 398-2998 Concordia: Library Building (1400 de Maisonneuve Blvd. W) 637, phone (514) 848-2424 ext. 3267 Email: I am a postdoctoral fellow at CICMA and McGill University , currently holding an FQRNT B3 postdoctoral fellowship (2004-2006). My research is in pure mathematics , more specifically in number theory (follow the research link below for more details). This term (Fall 2005) I am teaching MATH 570 (Higher Algebra I) . Upcoming: December 12 to December 16, 2005: Workshop on intersection of arithmetic cycles and automorphic forms , CRM, Universite de Montreal. Job application materials (new!) Research Teaching Expository talks (for research talks look here ) About me Various good people: Alberto De Sole Francois Blanchette Nora Ganter Peter McNamara
Glass, Darren
Columbia University. Arithmetic geometry.
Darren's Homepage Darren Glass I am no longer at Columbia. Now, my website and I can be found at Gettysburg College .
Girard, Martine
University of Sydney. Arithmetic of elliptic curves. Code to compute the heights of points on elliptic curves over number fields or function fields.
Martine Girard Martine Girard From January 2001 to June 2002, I was a postdoctoral fellow at Leiden University in the Netherlands. From October 2002 to March 2003, I was a postdoctoral fellow in Roma, at Tor Vergata University. Since the beginning of April, I am a postdoctoral fellow at the University of Sydney. You can contact me at the following addresses: Martine Girard School of Maths and Stats F07 The University of Sydney NSW 2006 Australia E-mail: girard@math.jussieu.fr girard@maths.usyd.edu.au Version franaise de cette page I did my PhD thesis under the supervisation of Marc Hindry and defended it in July 2000. My curriculum vitae in ps format. My papers: Group generated by the Weierstrass points of a plane quartic joint work with Pavlos Tzermias, in the Proceedings of the American Math Society 130 (2002), 667-672. Gomtrie du groupe des points de Weierstrass d'une quartique lisse in the Journal of Number Theory 94 (2002), 103-135. Groupe des points de Weierstrass sur une famille de quartiques lisses in Acta Arithmetica 105 (2002), 305--321. My preprints: A survey of the results up to June 2002 and of the techniques used The group generated by the Weierstrass points of some plane quartics . An explicit computation of this group for all curves with at least eight hyperflexes Group of Weierstrass points of a plane quartic with eight hyperflexes or more . Code for computing heights on elliptic curves with magma: You can find here some programs to compute the heights of points on elliptic curves over number fields or function fields. Back to the math institute home page
Garrett, Paul
University of Minnesota. Automorphic forms, representations, L-functions. Notes and papers.
Paul Garrett's Home Page [ Paul Garrett's Page ] "Be as honest as your conscience will allow." Carol Brunzell "An infallible method of conciliating a tiger is to allow oneself to be devoured." Konrad Adenauer "There are many truths, Lucinda. Some are uplifting, others are not." Uncle Bob, Plan 10 from Outer Space "If you tell the truth, you don't have to remember anything." Mark Twain "The law in its majestic equality forbids the rich as well as the poor from stealing bread, begging and sleeping under bridges." Anatole France [ambient page updated 12 Nov 05] ... [ home ] ... [ garrett@math.umn.edu ] [ Vignettes ] ... (updated 15 Sep 05) Automorphic forms, Representations, L-functions, Number Theory, Etc. [ Seminar ] ... (updated 09 Nov 05) [ Michael Harris' Ordway Lectures ] ... (updated 01 Feb 05) [ Buildings notes ] ... [ Old Automorphic Forms Bibliography ] ... [ Eisenstein series bibliography ] (2002) [ current students ] ... [ Ph.D. students ] ... [ REU students ] ... [ senior projects ] [ Abstract_Algebra ] ... [ Intro_Modular_Forms ] ... [ Functional_Analysis ] ... [ Number_Theory ] ... [ Complex_Analysis ] ... [ Crypto || Errata ] ... [ Coding || Errata ] ... [ Calculus_Notes ] ... [ Intro_Abstract_Algebra_Notes ] ... [ Notes_Archive ] [ Short intros ] to Emacs, HTML, .htaccess, TeX, xypic, Python, RCS, etc. [ perl snippets (etc.) ] ... [ applet to typeset tex ] ... [ graphing applet ] ... [ applet sampler ] ... [ meaningless graphics ] ... [ emacs in heck ] 1996-2005, Paul Garrett ... [ garrett@math.umn.edu ] [this page is http: www.math.umn.edu %7Egarrett ] The University of Minnesota explicitly requires that I state that "The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of Minnesota."
Fieker, Claus
Technische Universitt Berlin. Algebraic number theory; computational class field theory; the KANT computer algebra system.
Claus Fieker Claus Fieker Address: School of Mathematics and Statistics, F07 University of Sydney NSW, 2006 Australia phone: +61-2-9351 5795 fax : +61-2-9351 4534 email: claus AT maths.usyd.edu.au Research Interests: Algebraic Number Theory Computational Class Field Theory Computer Algebra MAGMA and KANT . Newly: computational mircobiology with my wife Michelle Publications Last modified: Fri Mar 12 19:03:03 MET DST 2004
Fischler, Stphane
Universit Paris-Sud. Arithmetic and algebraic geometry. Texts, lecture notes.
Stphane Fischler's homepage Stphane FISCHLER Equipe d'Arithmtique et de Gomtrie Algbrique Universit Paris-Sud Btiment 425 91405 Orsay Cedex, France 01 69 15 57 49 (from abroad: + 33 1 69 ...) - Room 144 stephane.fischler(AT)math.u-psud.fr Curriculum Vitae Mathematical Texts Conference "Young Researchers" on "Modular forms and transcendental number theory", organized with Samy Khmira and Eric Gaudron, C.I.R.M. (Luminy, near Marseilles), 26th - 30th May 2003. Teaching duties : Tutorials in Algebra Lectures for non-mathematicians Indo-french exchange programme French version. Please write to me if you have any problem with this webpage.
Flicker, Yuval
Ohio State University. Algebraic groups, symmetric spaces, Galois cohomology, automorphic forms, admissible representations of p-adic groups, trace formulae and bi-period summation formulae, their stabilization, and the fundamental lemma. Publications, resources, meetings, students.
Yuval Flicker -- Home Page Yuval flicker@math.ohio-state.edu Department of Mathematics, The Ohio State University, 231 W. 18th Ave., Columbus, OH 43210-1174 PHONES: (614) 292-5282(office); (614) 292-4975 (messages); (208) 247-5240 (efax); (614) 292-1479 (OSUfax) AUTOMORPHIC FORMS and SHIMURA VARIETIES of PGSp(2) World Scientific, August 2005 ARITHMETIC GEOMETRY SEMINAR at OSU COLLOQUIUM at OSU NUMBER THEORY SEMINAR at OSU RIGID ANALYTIC GEOMETRY STUDY GROUP at OSU TEACHING: feedback form - exam times ; - Math 104 ; - Math 150 ; - Math 152 ; - Math 161 ; - Math 255 ; - Math 530 ; - Math 568 ; - Math 571 ; - Math 672 ; - Math 771 ; - Math 841 ; - Math 981 GRADUATE STUDENTS: Ping-Shun Chan : Chan's thesis ; Dmitrii Zinoviev , cv ; Martin Nikolov ; Jennifer Orlich ; her Master thesis: "Spectral sequences and an application", in ps , and in pdf PUBLICATIONS: by date - by topic - MathSciNet - Curriculum Vitae - Current Research MATH: History - Number Theory - K-theory - Algebraic Geometry - AMS - Zentralblatt - UK - IHES - MPI - Oberwolfach - NSF - AAG - MathVirtualLib - MathArchives - OSUMathDept - OhioState - mathserialsonline - Oscar - ResearchFoundation - Library of Congress - Addison-Wesley - Books SMART LOGIC SOLUTIONS
Fukshansky, Lenny
Texas A+M University. Diophantine approximations, equations, and problems; Classical and adelic geometry of numbers; Quadratic and linear forms, polynomials; Theory of height functions, Mahler's measure, and connections with arithmetic geometry, Geometric combinatorics, lattices. Publications, talks.
index.html Lenny's Page Lenny Fukshansky Department of Mathematics 3368 TAMU Texas AM University College Station, TX 77843-3368 Phone: (979) 845-7797 Email: lenny@math.tamu.edu Office: Milner 209 I am a Visiting Assistant Professor at the Mathematics Department of Texas AM University . I received my Ph.D. in 2004 from the University of Texas at Austin (the irony!) under Professor J. D. Vaaler . My area of research is Number Theory , more specifically my interests are in Diophantine approximations, equations, and problems Classical and adelic geometry of numbers Quadratic and linear forms; polynomials Theory of height functions, Mahler's measure, and connections with arithmetic geometry Geometric combinatorics, lattices Here is my CV in .html format. Here are my publications: Algebraic points of small height with additional arithmetic conditions , Ph.D. Thesis, University of Texas at Austin, August 2004 ( pdf ) Small zeros of quadratic forms with linear conditions, Journal of Number Theory , vol. 108 no. 1 (2004), pg. 29-43 ( pdf ) (with Matthias Beck , Beifang Chen , Christian Haase , Allen Knutson , Bruce Reznick , Sinai Robins , and Achill Schuermann ) Problems from the Cottonwood Room , Contemporary Mathematics 374 (2005), 179-191 (Proceedings of the Summer AMS MAA SIAM Research Conference on Integer Points in Polyhedra, July 13 - July 17, 2003 in Snowbird, Utah) ( pdf - my section of this paper: Lattice points in homogeneously expanding compact domains ) Integral points of small height outside of a hypersurface , to appear in Monatshefte fr Mathematik ( pdf ) Siegel's lemma with additional conditions , to appear in Journal of Number Theory ( pdf ) On effective Witt decomposition and Cartan-Dieudonn theorem , to appear in Canadian Journal of Mathematics ( .pdf ) (with Sinai Robins ) Frobenius problem and the covering radius of a lattice , preprint ( .pdf ) Search bounds for zeros of polynomials over the algebraic closure of Q , in preparation Small zeros of quadratic forms over the algebraic closure of Q , in preparation Here are some of my recent talks: Some effective Diophantine results over the algebraic closure of Q , XXIVth Journes Arithmtiques , Marseilles, France, July 2005 ( .pdf ) Effective decompositions of quadratic spaces , ArithmeTexas , College Station, TX, April 2005 ( .pdf ) Counting lattice points in admissible adelic sets , MNTCG2 , Urbana-Champaign, IL, February 2005 ( .pdf ) Heights and Diophantine problems , September 2004, Colloquium , Rice University ( .pdf ) Siegel's lemma with additional conditions , June 2004, CNTA8 ( .pdf ) Integral points of small height outside of a hypersurface , May 2004, Illinois Number Theory Conference ( .pdf ) Small zeros of quadratic forms with linear conditions , June 2003, Mahler's Measure of Polynomials ( .pdf ) Here is the information about my teaching: Spring 2006: M662 (section 602) - Diophantine Approximations and Geometry of Numbers Fall 2005: M152H (sections 201 - 202) - Calculus II (Honors) Fall 2005: M304 (sections 502 - 503) - Linear Algebra Summer 2005: M662 (section 100) - REU VIGRE Course: Algebraic Methods in Computational Biology Spring 2005: M601 (section 602) - Methods of Applied Mathematics I Fall 2004: M601 (section 602) - Methods of Applied Mathematics I In 2004 - 2005 academic year I organized the Working Number Theory seminar. Here is some basic personal information about me. I am originally from St. Petersburg, Russia (this is not the best guide to the city, let's face it - hopefully I'll find a better one and remember to replace the link soon). I emigrated together with my family to San Francisco Bay Area (also not the best link) in 1990 - they still live there, so I visit there often. I went to college at UCLA (guess what was my major ). Oddly enough, my brother Roma studied at USC , but we do not fight over this - we have better reasons. My wife Eugenia is a math graduate student at the University of Texas, Austin . Here are some of my family pictures , and here is a link to our wedding album . I expect to put more information on this page later - possibly some of my favorite links as well as some of our pictures, so do check back. Free Satellite
Fuchs, Michael
Institute of Statistical Science, Academia Sinica. Probabilistic Number Theory; Continued Fractions and Metric Diophantine Approximation; Probability Theory for Weakly Dependent Random Variables; Analysis of Algorithms. Papers, thesis.
This page does no longer exist. In case you have questions, please contact webmaster AT geometrie.tuwien.ac.at
Fuchs, Clemens
Graz University of Technology. Number Theory; Algebraic Geometry; Coding Theory. Publications, thesis.
research.html Research Interests Number Theory: - Diophantine Equations - Subspace Theorem of W.M. Schmidt - Diophantine m-Tuples Algebraic Geometry: - Algebraic Function Fields and Applications - Diophantine Problems over Function Fields Coding Theory: - Geometric Goppa-Codes - AG-Codes due to Xing, Niederreiter, Lam Publications Algebraisch-geometrische Codes, Diplomarbeit, TU Wien, 2000. ( dvi , pdf ) Quantitative finiteness results for Diophantine equations, PhD-Thesis (Dissertation), TU Graz, 2002. ( dvi , pdf ) On the Diophantine Equation G_{n}(x)=G_{m}(P(x)), joint work with A. Peth and R. F. Tichy Monatsh. Math. 137 (2002) 3, 173-196 Preprint: ( dvi , pdf ) Diophantine m-tuples for linear polynomials, joint work with A. Dujella and R. F. Tichy Period. Math. Hungar. 45 (1-2) (2002), 21-33 Preprint: ( dvi , pdf ) Perfect powers in linear recurring sequences, joint work with R. F. Tichy Acta Arith. 107.1 (2003), 9-25 Preprint: ( dvi , pdf ) An upper bound for the G.C.D. of two linear recurring sequences Math. Slovaca 53 (2003), No. 1, 21-42 Preprint: ( dvi , pdf ) On the equation G_{n}(x)=G_{m}(P(x)): Higher order recurrences, joint work with A. Peth and R. F. Tichy Trans. Amer. Math. Soc. 355 (2003), 4657-4681 Preprint: ( dvi , pdf ) A Polynomial Variant of a Problem of Diophantus and Euler, joint work with A. Dujella Rocky Mountain J. Math. 33 (2003), 797-811 Preprint: ( dvi , pdf ) Polynomial-exponential equations and linear recurrences Glasnik Mat. Ser. III 38 ( 58) (2003), 233-252 Preprint: ( dvi , pdf ) On the equation G_{n}(x)=G_{m}(P(x)) for third order linear recurring sequences Port. Math. (N.S.) 61 (2004), 1-24 Preprint: ( dvi , pdf ) Complete solution of the polynomial version of a problem of Diophantus , joint work with A. Dujella J. Number Theory 106 (2004), 326-344 Preprint: ( dvi , pdf ) Polynomial-exponential equations involving several linear recurrences, joint work with A. Scremin Publ. Math. Debrecen 65 1-2 (2004), 149-172 Preprint: ( dvi , pdf ) Diophantine inequalities involving several power sums , joint work with A. Scremin Manuscripta Math. 115 (2004), 163-178 Preprint: ( dvi , pdf ) Complete solution of a problem of Diophantus and Euler , joint work with A. Dujella J. London Math. Soc. (2) 71 (2005), 33-52 Preprint: ( dvi , pdf ) Diophantine problems with linear recurrences via the Subspace Theorem Integers: Electronic Journal of Combinatorial Number Theory 5(3) (2005), A08. Preprint: ( dvi , pdf ) Effective bounds for the zeros of linear recurrences in function fields , joint work with A. Peth To appear in J. Thor. Nombres Bordeaux ( dvi , pdf ) On a family of Thue equations over function fields , joint work with V. Ziegler To appear in Monatsh. Math. ( dvi , pdf ) Thomas's Family of Thue equations over function fields , joint work with V. Ziegler To appear in Q. J. Math. (Oxford) ( dvi , pdf ) On the Diophantine equation G_n(x)=G_m(y) with Q(x,y)=0 , joint work with A. Peth and R. F. Tichy Manuscript ( dvi , pdf ). D iophantine m-tuples for linear polynomials. II. Equal degrees , joint work with A. Dujella and P.G. Walsh Manuscript ( dvi , pdf ). Substitutions, abstract number systems and the space filling property , joint work with R. Tijdeman Manuscript ( dvi , pdf ). Polynomial-exponential equations involving multi-recurrences Manuscript ( dvi , pdf ). Effective Solution of the D(-1)-quadruple Conjecture , joint work with A. Dujella and A. Filipin Manuscript ( dvi , pdf ). Copyright notice: Material on this page is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. Last modified on 14.11.2005 by Clemens Fuchs
Fisher, Tom A.
University of Cambridge. Arithmetical algebraic geometry, specifically descent calculations for elliptic curves. Papers, slides, notes.
Dr T.A. Fisher Department of Pure Mathematics and Mathematical Statistics DPMMS People Dr T.A. Fisher Dr T.A. Fisher Title:University Lecturer Email: T.A.Fisher@dpmms.cam.ac.uk College:Trinity College Room: E1.09 Tel: +44 1223 764275 Personal Home Page Research Interests: My research interests are in arithmetical algebraic geometry, specifically descent calculations for elliptic curves. This means that I am interested in making practical the computation of Selmer groups for elliptic curves over number fields, and in using geometric methods to investigate the Tate-Shafarevich group. 2003-2005 Department of Pure Mathematics and Mathematical Statistics, University of Cambridge Information provided by webmaster@dpmms.cam.ac.uk
Fermigier, Stfane
Number theory and algebraic geometry.
Warning! The pages you are about to enter have been written between 1994 and 1996, and have not been updated since . These pages are not up to date. If you want to find up to date information about what I'm doing right now, go to Nuxeo.com instead (basicallly, we are doing Zope and Python development). So, do you really want to see Stfane Fermigier's home site circa 1995 ? Yes (french version) Yes (english version) No Other sites maintained by Stfane Fermigier: Nuxeo , my company. Portalux , the Linux portal. NewsFR , daily news from many sources, in french. LinuxSlides , the virtual Linux conference. Other sites that I've been contributing to: AFUL , the french speaking Linux and free software users association.
Ellenberg, Jordan
University of Wisconsin - Madison. Arithmetic algebraic geometry. Publications, teaching, collaborative research laboratory.
Jordan S. Ellenberg Assistant Professor of Mathematics 323 Van Vleck Hall Department of Mathematics University of Wisconsin 480 Lincoln Drive Madison, WI 53706 e-mail: ellenber@math.wisc.edu I've been teaching at Wisconsin since the fall of 2005. My field is arithmetic algebraic geometry: my specific interests include rational points on varieties, enumeration of number fields and other arithmetic objects, Galois representations attached to varieties and their fundamental groups, non-abelian Iwasawa theory, automorphic forms, Hilbert-Blumenthal abelian varieties, Q-curves, curves of low genus, Serre's conjecture, the ABC conjecture, and Diophantine problems related to all of the above. My research here is partially supported by an NSF-CAREER grant and a Sloan Research Fellowship. In Fall 2005, I am teaching Math 491, a topics course in number theory, and Math 847, a graduate topics course about rational points on varieties over global fields. This set of notes from the 2002 AIM conference on rational points provides a useful overview of questions and techniques people are thinking about in this area; the list of open problems is especially recommended. I am also running the Collaborative Undergraduate Research Laboratory, in which teams of undergraduates are investigating questions about the distribution of invariants of cubic number fields; see our course blog to follow our progress. I wrote a novel called The Grasshopper King , which came out in 2003 from Coffee House Press . I used to live in Princeton, NJ; a popular feature of my old web page was How to Eat Dinner in Princeton . Warning: this page is accurate only up to August 2005. Papers and Preprints My CV ( .dvi version or .pdf version ) Personal Page Teaching Barry Mazur's Mathematical Genealogy Back to math department home page Send me e-mail Jordan Ellenberg * ellenber@math.wisc.edu * revised 5 Sep 2005
Eikenberg, EdwardV.
University of Maryland. Ranks of elliptic curves. Lecture notes.
Ed Eikenberg's Homepage Welcome to the Homepage of Ed Eikenberg Edward V. Eikenberg Graduate Student University of Maryland Mathematics Department Ed_Hokie@terpalum.umd.edu Notes from my PME talk on Congruent Numbers and Elliptic Curves My Ph.D. Dissertation: Rational Points on Some Families of Elliptic Curves Teaching Stuff: I am no longer at the University of Maryland, but I was a TA there for several years. For the record, here is a list of the courses I have taught: Fall 1996 Math 140 - Calculus I Spring 1997 Math 141 - Calculus II Fall 1997 Grading and Tutoring Spring 1998 Grading and Tutoring Fall 1998 Math 140 - Calculus I Spring 1999 Math 110 - Elementary Math Models Fall 1999 Math 141 - Calculus II Spring 2000 Math 140 - Calculus I Summer II 2000 Math 406 - Intro to Number Theory Fall 2000 Math 110 - Elementary Math Models Spring 2001 Math 110 - Elementary Math Models As a special note, I would like to thank the students from my 1999 classes for nominating me for the Math Department's Excellence in Teaching Award for TA's. I was not the winner of the award, but I was one of the two TA's who received an Honorable Mention. Thank you all so much. I wish you and all of my current and previous students success in all of your ventures. My Life Before Graduate School: Baltimore, MD is my hometown, and I am a big Orioles fan. I usually go to about 5-10 games a year, and watch them whenever I can. I am also a fan of the Baltimore Ravens, and try to follow the Washington Redskins as well. I went to high school at Calvert Hall , an all-male, private, Catholic, college-preparatory high school located in the Towson area of Baltimore County. I received my bachelors degree in math from Virginia Tech in December of 1992. I am a huge fan of the VT football team, the Hokies! They just completed one of their best seasons ever, going 11-0 before losing to Florida State in the Sugar Bowl for the NCAA national championship. Of course I took a road trip to New Orleans for the game. Even though they lost, I had a great time. I can't wait for next season. After graduating from college, I went to work at Watson Wyatt Worldwide . I worked there as an actuarial technician for almost 2 years full time before I cut back to a part-time status and started graduate school. I still work there occasionally, on an as-needed basis. My Life During Grad School: For those who don't know me, I'm a grad student at University of Maryland, College Park working on my Ph.D. in mathematics. My current area of research is ranks of elliptic curves. An elliptic curve is a cubic polynomial function whose rational points form a finitely-generated group under an appropriate operation. For more detailed info on what an elliptic curve is, check out the notes from my PME talk on congruent numbers and elliptic curves . I am currently studing the ranks of these groups as related to the curve. In particular, I am concentrating on techniques to find the rank without actually finding points that generate the group. So I spend lots of time doing research toward my dissertation. One day, I may even finish. My favorite diversion from my research is playing volleyball. In fact, you might even say that my favorite diversion from volleyball is doing math research. I am a volleyball fanatic. I play in a league almost all year round and play doubles tournaments in the summer. Basically, I play way more than I should. I also enjoy playing tennis, racquetball, ultimate frisbee, and softball. Basically, I love outdoor activities. University of Maryland || UM Math Dept Homepage
Elsholtz, Christian
Royal Holloway, University of London. Elementary, combinatorial, and analytic number theory, additive and multiplicative problems.
Elsholtz Christian Elsholtz Employment: 1997 99: Wissenschaftlicher Mitarbeiter, University of Stuttgart 1999 2003 Wissenschaftlicher Assistent, Technical University of Clausthal 2003-today: Lecturer in Pure Mathematics at Royal Holloway, University of London. Degrees: Diploma in Mathematics, 1996, Technical University of Darmstadt. Ph.D., 1998, Technical University of Darmstadt. Subject: Sums of k Unit Fractions. My Ph.D. ancestors Habilitation Privatdozent 2002, Technical University of Clausthal. Title: Combinatorial prime number theory- A study of the gap structure of the set of primes. Comments: I am occasionally asked: "what is Habilitation?" The Habilitation is a formal degree based on postdoctoral work, and is considered to be more significant than a Ph.D. In the German system it is the highest scientific qualification. It consists of a written Thesis, a talk on current research including an oral exam, and a lecture to demonstrate teaching skills. For each of the latter two talks I had to submit three distinct subjects (covering the whole range of mathematics) of which the faculty chose: The crossing number in graph theory and its applications, and Fair division of sandwiches and cakes. Address: Department of Mathematics Royal Holloway, University of London Egham Surrey TW20 0EX UK. Phone: ++44 1784 414021 Fax: +44 1784 430766 eMail: . AT-symbol . . Fields of Interest: Elementary, combinatorial, and analytic number theory, additive and multiplicative problems Combinatorial group and ring theory Graph Theory, combinatorics and geometry (in particular extremal graph theory) my number theoretical interests in detail: Applications of sieve methods, in particular of the large sieve. The additive structure of the set of primes. Additive decomposition of sets (in particular the set of primes). Prime k tuple conjecture. Detection of large structures in "unstructured" sets (like the primes). Diophantine equations. Sums of unit fractions. Sums and products of sets of integers. Zero sums (Erdos-Ginzburg-Ziv-type theorems). Sums of two squares. Computational methods. my algebraic interests detail: Zero sums in abelian groups Z_n^d. Generators of cyclic groups. How many elements are necessary to ensure the existence of certain substructures? Combination of additive and multiplicative properties in rings. my combinatorial interests in detail: Extremal graph theorey. (Forbidden substructures). Kvari-Sos-Turan type theorems. The cube lemma. Algorithmic approaches to the topics above. Crossing numbers of graphs. Lattice point problems, geometric problems. Regular structures in "unstructured" sets. Here is a link to a list of my scientific work. Teaching material. I organise the Pure Maths seminar at Royal Holloway. Collection of useful links (books, journals, dictionaries etc). Number theory day 2003. Workshop analytische Zahlentheorie (3.-7. April 2000) Ntzliche Links besonders im Bereich Mathematik Bibliotheken Zeitschriften Bcher
Elkies, Noam D.
Harvard. Number theory, algebraic geometry. Preprints, tables in computational number theory.
Noam D. Elkies Home Page Noam D. Elkies Professor, Department of Mathematics , Harvard University . E-Mail: elkies@math.harvard.edu Work Address: Department of Mathematics, Harvard University, Cambridge, MA 02138. Work Telephone: (617) 495 4625; fax: (617) 495 5132 Mathematics papers links Music scores links Chess links Miscellaneous writings etc. Please ignore these HTML tests. sample link 1 sample link 2 sample link 3(?)
Drmota, Michael
Institut fr Diskrete Mathematik und Geometrie, TU Wien. Number Theory; Combinatorial Enumeration and Analysis of Algorithms; Stochastic Processes in Combinatorial Structures. Publications, teaching.
Institute of Discrete Mathematics and Geometry Sorry. This website uses frames that your browser cannot display. Please go here
Deligne, Pierre
Institute for Advanced Study. Publications, preprints.
Pierre Deligne Office Fuld Hall 210 Mailing Address School of Mathematics Institute for Advanced Study Einstein Drive Princeton N.J. 08540 e-mail Academic Assistant: Dottie Phares (609) 734-8113 Curriculum Vitae Publication List Preprints
Diamond, Harold G.
University of Illinois at Urbana-Champaign. Analytic number theory, distribution of primes, arithmetic functions, sieve methods. Publications.
Harold G. Diamond Harold G. Diamond Professor Emeritus, Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana, Illinois 61801-2975 Office: 329 IlliniHall ; (217) 333-8937; FAX: (217) 333-9576 e-mail: diamond@math.uiuc.edu General Information B.A. Cornell University, 1961. Ph.D. Stanford University, 1965. UIUC faculty member since 1967. Visiting Appointments: E.T.H. (Zurich), Institute for Advanced Study, University of Nottingham, University of Paris, University of Texas, University of Ulm. Research Analytic number theory, distribution of primes, arithmetic functions, sieve methods. Selected Papers Text ANALYTIC NUMBER THEORY An Introductory Course, by Paul T. Bateman Harold G. Diamond, Sept., 2004. World Scientific Publishing Co. Comments and Corrigenda Number Theory Foundation Foundation Website Academic Family Tree Ph.D. Ancestors 1st Generation Ph.D. Descendents Putnam Exam Problem Contests Information
Diamond, Fred
Brandeis University. Modular forms and Galois representations. CV, publications and preprints.
Mathematics Department Fred Diamond | Brandeis University Jump to content - Jump to section navigation About Brandeis Admissions Campus Life Academics Research Alumni Offices News Events Keyword: Mathematics Department About the Department Home Page Contacts News Older News Items Directions Map Site Credits People Faculty Graduate Students Former Graduate Students Staff Undergraduate Current Courses Bulletin Program Description Undergraduate Handbook Placement Undergraduate Activities Putnam Exam Graduate Current Graduate Courses Bulletin Program Description Brandeis Graduate School On-line Application Forms Graduate School Association Mathematics Graduate Student Council Graduate Student Seminar Seminars Colloquia Fellowship of the Ring Everyperson Topology Heegaard-Floer Theory Colloquium Other Events Gazette Resources Links Science Library MathSciNet ArXiv Gazette Colloquium Mathematics WWW Servers Department Contacts News Events Directions Math Placement Exam Department of Mathematics Brandeis University 415 South Street MS 050 Waltham, MA 02454 781.736.3050 fax 781.736.3085 maths@brandeis.edu Fred Diamond Department of Mathematics Brandeis University, MS 050 Waltham, MA 02454-9110 Office: Goldsmith 204 Phone: (781)736-3063 Fax: (781)736-3085 email: fdiamond@brandeis.edu My main area of research is number theory, especially modular forms and Galois representations. Here are my CV , publications and preprints. Teaching schedule, Spring 2002: Math 30B, Algebra II, TF 12:10-1:30. USEM 10B, Reading, Writing and Arithmetic, TF 3:10-4:30. This page was last modified on September 02, 2005 About Brandeis Admissions Campus Life Academics Research Alumni Offices News Events Site Copyright 1997 - 2005 Brandeis University, All Rights Reserved Copyright Policy Contact Us
Diem, Claus
Institute for Experimental Mathematics, University of Essen. Arithmetic algebraic geometry: structure and arithmetic of abelian varieties; discrete logarithm problems; the regular inverse Galois problem. Publications, thesis.
Claus Diem Claus Diem I am now with the University of Leipzig. My new homepage is here. Ich arbeite nun an der Universitt Leipzig. Meine neue Heimseite ist hier .
Dienst, Thilo
Universitt Dortmund. Geometry of Numbers; Polytopes; Quadratic Forms; Diophantine Approximation; History of Mathematics. Publications, thesis, resources.
Thilo Dienst, Institut fr Algebra und Geometrie
Deng An-Wen
Academica Sinica, Taiwan. Number Theory and Algebraic Geometry. Publications.
An-Wen Deng An-Wen Deng @@An-Wen Deng received a B. S. degree in Mathematics from the Central University in 1987. In 1989 he got M. S. from Tsinghua University. At the end of 1991 he went to Germany to go on studying Mathematics. In 1997 he received a doctoral degree. His research interests are centered about Number Theory and Algebraic Geometry. He enjoys mountaineering, reading history. During his stay in Germany he did some aid for the international amnesty and helped the political refugee. Publications Varietat mit der Hardy-Littewoodschen Eigenschaft, Mathematica Gottingensis. Heft 21(1997).
Diaz y Diaz, Francisco
Universit Bordeaux I. Computations in number fields. Preprints.
Page maison de Francisco Diaz y Diaz Page maison de Francisco Diaz y Diaz Universit Bordeaux I UFR de Mathmatiques et Informatique 351, cours de la Libration F - 33405, Talence cedex Tl: +33 05 56 84 64 38 Fax : +33 05 56 84 69 50 diaz@math.u-bordeaux.fr I am professor of mathematics at the University of Bordeaux I. My field of research is Number Theory ans more particularly Algebraic Number Theory. I am interested by all kind of computations in number fields. In the past years I have organized the Seminar on algorithmic. If you want to know the history of this seminar, click here or here to obtain the list of the speakers of the past years. Recent publications or preprints (does not include published papers). Corps imprimitifs de degr 9 de petit discriminant (with M. Olivier), Preprint. Introduction au langage de la th orie des nombres Course given at the Etats de la Recherche, 1995, preprint. Tables of octic fields with a quartic subfield (with H. Cohen and M. Olivier), Math. Comp., submitted. Algorithmic methods for finitely generated Abelian groups (with H. Cohen and M. Olivier), J. Symb. Comp., submitted. Computing ray class groups, conductors and discriminants (with H. Cohen and M. Olivier), preprint. Approche algorithmique du groupe des classes logarithmiques (with F. Soriano), preprint WWW page design par Thomas Papanikolaou Francisco Diaz y Diaz Dernire mise jour le 4 fvrier 1998.
Dresden, Greg
Washington and Lee University. Mahler measure of polynomials. Publications.
Dr. Dresden's Home Page Dr. Gregory Dresden, 2005-06 Department of Mathematics Washington Lee University (540) 458-8806 Yes, that really is me in the picture! It was taken at Larabee State Park , a favorite spot of mine that is near a favorite city of mine, Bellingham, WA. To find out more about me, be sure to check out my mostly-up-to-date Curriculum Vitae [pdf file]. To see me in action, this short film clip (requires Quicktime ) from a WL fundraising video shows me discussing a linear algebra class I designed a few years back. How To Reach Me Office Location: Robinson Hall R-1 (I'm on the first floor now!) Office Phone: (540) 458-8806. FAX: (540) 458-8239. Mailing Address: Department of Mathematics , Washington and Lee University , Lexington VA 24450. I generally tend to avoid using e-mail, as it seems so impersonal (and I don't like to type, either!), but if you must, you can e-mail me at dresdeng "at" wlu.edu. Just be sure to include a phone number or address, so that I can call write you back. Also, if you don't hear from me after a few days, it's probably because your e-mail got deleted by my automatic spam filter. Try to send it again as a plain-text message, or just call me on the phone. Teaching Schedule and Class Information Math 101-Z (Calculus I), 9-10:00, M, T, W, F, in R-25 (second floor). Math 101-Z (Calculus I), 10-11:00, M, T, W, F, in R-6 (first floor). Math 121 (Discrete math), 12-1:00, M, T, W, F, in R-7 (first floor). Math 493 (Honors thesis), by arrangement. Office Hours (These are subject to change, and you can always make an appointment to see me.) Monday, 3 p.m. Wednesday, 11 a.m. Thursday, 12 p.m. Friday, 4 p.m. ...and one "floating" office hour, per week, by appointment Small Rings Along with Professor Siehler , my Abstract Algebra students and I are working on finding natural representations for finite rings. Please visit our Small Rings page for examples. Mathematical Research I work in an area of mathematics called number theory, and in particular on the subject of the Mahler measure of a polynomial. I also study other topics from both number theory and abstract algebra (on polynomials, groups, algebraic extensions, etc). Here are some of the articles I have written: Orbits of Algebraic Numbers with Low Heights, Math. Comp. 67 (April 1998), 815--820. (Download as: pdf , LaTeX , dvi , ps .) Two Irrational Numbers From the Last Non-Zero Digits of n! and nn, Math. Mag. 74 (October 2001), 316--320. ( pdf , LaTeX .) Sums of Heights of Algebraic Numbers, Math. Comp., 72 (2003), 1487--1499. ( pdf , LaTeX , dvi , ps .) On the Middle Coefficient of the Cyclotomic Polynomial, MAA Monthly 111 (June-July 2004), 531--533. ( pdf , LaTeX .) The above article led to a new sequence in ATT's On-Line Encyclopedia of Integer Sequences , with the not-very-descriptive name A094754 ; see also the related sequence A095877 . Thanks to T. D. Noe for submitting these to the encyclopedia (and to ATT for hosting such a fun and valuable resource). There Are Only Nine Finite Groups of Linear Fractional Transforms with Integer Coefficients, Math. Mag. 77 (June 2004), 211--218. ( pdf , LaTeX .) Finding Factors of Factor Rings over the Gaussian Integers, with Wayne Dymacek , MAA Monthly 112 (Aug-Sep, 2005), 602--611. ( pdf , LaTeX .) The above article gives me an Erds number of 4, based on the (probably non-unique) chain: Greg Dresden -- Wayne Dymacek -- Gerard Chang -- Stephen Hedetniemi -- Paul Erds. This article was inspired by questions from students Matt Kozora and Michael Riley in Professor Dymacek's Math 322 class. Three Transcendental Numbers From the Last Non-Zero Digits of nn, Fn, and n!, submitted to Mathematics Magazine. A Combinatorial Proof of Vandermonde's Determinant, with Art Benjamin , submitted to the MAA Monthly. A New Approach to Rational Values of Trigonometric Functions, preprint. On the Mahler Measure of P(f g), preprint. ( pdf , LaTeX , ps .) For information on the Mahler measure, please check out this excellent web site prepared by Mike Mossinghoff, a fellow Texas graduate (now at Davidson). I co-hosted the SERMON 2003 math meeting, a regional number theory conference. Check it out! I've given many presentations on mathematics and one on teaching mathematics, at local and national conferences. Also, Art Benjamin (mentioned above) gave a presentation on our joint work at MIT in December of 2004, and fellow WL professor Wayne Dymacek gave a talk on our joint paper here at WL. In the first half of 2005, I gave a talk in Columbia (South Carolina) on transcendental numbers, and a talk in Charlottesville (Virginia) on Gaussian integers. Math Information for Washington Lee Students (and others) An extremely cool reference on the web is Eric Weisstein's World of Mathematics , hosted by the nice folks at Wolfram Research. Be sure to check out my Winter Term Linear Algebra Page , with all of its cool math videos done by students. This led to a presentation at the San Diego AMS MAA meeting on the innovative use of student-produced video in a math class, and may soon end up as a paper, as well. My Math Department actuary web page tells you everything you want to know about how to pursue this lucrative and rewarding career (and yes, we have math classes for that). Anticipating having trouble with Calculus 101 or 102? You might want to check out the free nightly tutoring sessions in Robinson 6, Sunday through Thursday from 7 to 8:30 pm. A favorite course of mine is Math 365. This is an introductory course in number theory, a very beautiful area of mathematics that dates back to the ancient Greeks, yet contains many modern applications ranging from deciphering German codes during WWII to verifying the account numbers on your ATM card. Students who took this course during Winter term really enjoyed it. I occasionally teach Math 195, on cryptography and number theory, in the spring term. This course covers many of the issues concerning the current encryption methods used by commercial programs and by the military: how the codes work, why they work, and how to break them. Surprisingly, one can create very secure (but not perfectly secure!) encryption systems using some fairly easy facts of basic number theory about prime numbers. An excellent example of an encryption system is the PGP system by Phil Zimmermann. So secure is Zimmermann's PGP program that the U.S. government classified it as a restricted munition, and tried to keep him from sharing it with folks in foreign (and potentially hostile) nations. Indeed, many fear that terrorists and criminals can use these systems to encrypt their files, thus making recovery nearly impossible. The most exciting part of the course, I think, is our field trip to the Marshall Museum, which has an extensive collection of cryptographic materials and artifacts. In this picture from a few years back, Dr. Dymacek (on the right) explains to us some of the details about the ENIGMA machine. You'll recall that the ENIGMA was used by the Germans to encode military messages during the war. British and American scientists (led by the brilliant Alan Turing) managed to break the code, and thus tremendously advanced the Allied war effort. Background I've spent far too many years studying mathematics in school, starting with Stanford University for my bachelor's, followed by the University of Wisconsin at Madison for my master's degree and the University of Texas at Austin for my doctorate, under the guidance of Dr. Jeffrey Vaaler. In between, I spent a year teaching at a Texas high school called St. Stephen's . Once I got my Ph.D., I came here to Washington Lee University , where I am joined by many Texans, including my wife, a shy San Antonio girl who won't let me put her picture on the web. So, I've found a reasonable facsimile in her comic namesake, Veronica , who shares with my wife the raven hair and general all-around cuteness. As for myself, I'd say that Jason Fox best represents my nerdy demeanor and my affinity for all things scientific. Links For general mathematical information, here are some of my favorite links: The Association for Women in Mathematics has many wonderful programs to encourage women in pursuing a career in the mathematical sciences. AWM student membership is only $15, and yes, men can join too! MAA Online , from the Mathematical Association of America, has many great links to career and grad school information. MAA student membership is $25, and well worth it. The AMS Home Page , from American Mathematical Society, contains valuable professional information, along with a searchable index to mathematical articles. Here is a direct link to the MathSciNet search page . If you're thinking of going to graduate school, you might want to look into getting an AMS student membership , at around $38 or so. (I'm a member of all three groups.) Mathematics Information Servers is a giant listing of just about every mathematical group you can imagine, including a world-wide list of on-line college and university mathematics departments. This is very helpful in providing a direct link to math professors and programs around the world. Here's a direct link to the Number Theory web . Texas has a nice listing of US cc's, colleges, and universities . Locally, check out Washington Lee's expanded access to JSTOR , which provides free access to many math and science journals, in printer-ready, xerox-quality form. This is not a math-related link, but if you want to know what's happening on campus, check out the (text-based) master calendar . This page was written in HTML by Dr. Gregory Dresden, using a template originally borrowed from UT-Austin . Tuesday, April 19, 2005. Department of Mathematics at Washington Lee University
Denef, Jan
University of Leuven. Number Theory, Algebraic Geometry, Singularity Theory and Mathematical Logic. Publications, software.
jan homepage Home Page of Jan Denef Hello! At work! Contents Work information Contact information Recent publications (since 1995) (3 new items) Electronic version of some older publications Complete publication list till 1994 Remarks to some of my papers Slides of some of my lectures Software developed under my direction (1 new item) Ph.D. theses under my direction (2 new items) Links to co-authors Other links Last Revised: January 21, 2005. Work Information Job title Full Professor of Pure Mathematics. Department University of Leuven , Department of Mathematics , Section of Algebra , Research Unit Algebraic Geometry and Number Theory Fields of Research Number Theory, Algebraic Geometry, Singularity Theory and Mathematical Logic. Specific Research Topics Computational Number Theory, Igusa's Local Zeta Function and motivic analogues, Motivic and p-adic integration, Cohomological Study of Trigonometric Sums, Etale Cohomology, Monodromy, Asymptotics of Oscillating Integrals and Newton Polyhedra, Hilbert's Tenth Problem, Quantifier Elimination, Subanalytic Sets and Model Theory. Back to top Contact Information Address University of Leuven, Department of Mathematics, Celestijnenlaan 200 B, B-3001 Leuven (Heverlee), Belgium. Electronic mail address jan.denef@wis.kuleuven.ac.be Web address http: www.wis.kuleuven.ac.be wis algebra denef.html Office phone : (+32)16-327010 Office fax : (+32)16-327998 Home phone : (+32)16-228587 Back to top Recent Publications (since 1995) R. Cluckers, J. Denef, Orbital integrals for linear groups . Preprint July 2005. J. Denef, F. Vercauteren, Computing zeta functions of Cab curves using Monsky-Washnitzer cohomology . Preprint February 2004. J. Denef, J. Nicaise, and P. Sargos, Oscillating integrals and Newton polyhedra (new extended version) , to appear in Journal d'Analyse Mathmatique. J. Denef and F. Vercauteren, An extension of Kedlayas algorithm to hyperelliptic curves in characteristic 2 , to appear in Journal of Cryptology. J. Denef and F. Loeser, On some rational generating series occuring in arithmetic geometry , in Geometric Aspects of Dwork Theory, edited by A. Adolphson, F. Baldassarri, P. Berthelot, N. Katz and F. Loeser, volume 1, de Gruyter, 509-526 (2004). J. Denef and F. Vercauteren, An extension of Kedlayas algorithm to Artin-Schreier curves in characteristic 2 . In C. Fieker and D.R. Kohel, editors, Algorithmic number theory. 5th international symposium. ANTS-V, volume 2369 of Lecture Notes in Computer Science, pages 308-323. Springer-Verlag Berlin, 2002. J. Denef and F. Loeser, Motivic integration and the Grothendieck group of pseudo-finite fields , Proceedings of the International Congress of Mathematicians ( ICM 2002 ), Beijing 2002, Volume 2, 13-23, Higher Education Press, Beijing 2002 . J. Denef and F. Loeser, Macdonald integrals and monodromy , International Journal of Mathematics 12 (2001), 987-1004. J. Denef and S. Sperber , Exponential sums mod p^n and Newton polyhedra . A tribute to Maurice Boffa, Bulletin of the Belgian Mathematical Society --Simon Stevin 2001, suppl., 55-63. J. Denef, J. Van Geel, L. Lipshitz, and T. Pheidas, editors: Hilbert's Tenth Problem: Relations with Arithmetic and Algebraic Geometry , Contemporary Mathematics, 270 (2000), 367 pp. This is the proceedings of a conference at the University of Gent, November 2-5, 1999. J. Denef and H. Schoutens , On the decidability of the existential theory of Fp[[t]] , Valuation Theory and its Applications, Volume II, ed. F.-V. Kuhlmann, S. Kuhlmann and M. Marshall, Fields Institute Communications 33, American Mathematical Society 2003, pp. 43-60. J. Denef and F. Loeser, Geometry on arc spaces of algebraic varieties , European Congress of Mathematics, Vol. 1 (Barcelona, 2000) , 327-348, Progr. Math., 201, Birkhuser, Basel, 2001. J. Denef and K. Hoornaert, Newton polyhedra and Igusas local zeta function , Journal of Number Theory 89 (2001), 31-64. J. Denef and F. Loeser , Lefschetz numbers of iterates of the monodromy and truncated arcs , Topology 41 (2002), 1031-1040. J. Denef and F. Loeser, Definable sets, motives and p-adic integrals , Journal of the American Mathematical Society 14 (2001), 429-469. J. Denef and F. Loeser , Motivic integration, quotient singularities and the McKay correspondence , Compositio Math. 131 (2002), 267-290. J. Denef and F. Loeser, Motivic exponential integrals and a motivic Thom-Sebastiani Theorem , Duke Mathematical Journal 99 (1999), 285-309. J. Denef, Arithmetic and Geometric Applications of Quantifier Elimination for Valued Fields , Model Theory, Algebra, and Geometry, ed. D. Haskell ,A. Pillay, and C. Steinhorn, Cambridge University Press , Math. Sci. Res. Inst. Publ. 39 (2000),173-198. J. Denef and P. Jacobs, On the vanishing of Principal Value Integrals , Comptes Rendus de l' Acadmie des Sciences de Paris 326 (1998), 1041-1046. J. Denef, A. Laeremans and P. Sargos, On the largest nontrivial pole of the distribution |f|^s , RIMS Kokyuroku 999 (1997), 1-9. J. Denef and F. Loeser, Germs of arcs on singular algebraic varieties and motivic integration , Inventiones Mathematicae 135 (1999), 201-232. J. Denef and F. Loeser, Motivic Igusa zeta functions , Journal of Algebraic Geometry 7 (1998), 505-537. J. Denef and F. Loeser, Character sums associated to finite Coxeter groups , Trans. Amer. Math. Soc. 350 (1998), 5047-5066. J. Denef and A. Gyoja, Character sums associated to prehomogeneous vector spaces , Compositio Math. 113 (1998), 273-346 . J. Denef, Poles of p-adic Complex Powers and Newton Polyhedra, Nieuw Archief voor Wiskunde (4), 13 (1995), 289-295. J. Denef and W. Veys, On the holomorphy conjecture for Igusa's local zeta function, Proc. Amer. Math. Soc., 123 (1995), 2981-2988. J. Denef and F. Loeser, Regular elements and monodromy of discriminants of finite reflection groups, Indagationes Math. (N.S.) 6 (1995), 129-143. Back to top Electronic versions of some older publications J. Denef, Report on Igusa's Local Zeta Function , Sminaire Bourbaki 43 (1990-1991), exp. 741; Astrisque 201-202-203 (1991), 359-386. Back to top Complete publication list till 1994 Publications of Jan Denef from 1974 till 1994 Back to top Remarks to some of my papers Click here for the remarks Back to top Slides of some of my lectures My lectures at the Newton Institute for Mathematical Sciences, August 2000: Geometry On Arc Spaces My lecture at the International Congress of Mathematicians ( ICM 2002 ), Beijing 2002: Motivic integration and the Grothendieck group of pseudo-finite fields Back to top Software developed under my direction POLYGUSA : A computer program to calculate Igusas local zeta function and the topological zeta functions of a polynomial that is nondegenerate with respect to its Newton polyhedron. The program is written in Maple V 5.1 for Windows and was developed by K. Hoornaert and D. Loots, under my supervision. LogicPalet : A computer program designed to help students master the basic concepts of mathematical logic, with emphasis on the semantic aspects of it. It is written by Jan Denef. Back to top Ph.D. theses under my direction Ph.Jacobs (1998), A. Laeremans (1997 ), H.Schoutens (1991), W.Veys (1991), L.Lauwers(1990), J.Pas(1989), D.Bollaerts(1988), A. Herremans (2001), K. Hoornaert (2002), R. Cluckers (2002), F.Vercauteren (2003), J. Nicaise (2004) In preparation: A. Commeine, W. Castryck, H. Hubrechts. Back to top Links to co-authors F.Loeser , A.Gyoja , W.Veys , Ph.Jacobs , K.Hoornaert , P.Sargos , L.Lipshitz , H.Schoutens, S.Sperber, F.Vercauteren Back to top Some other links Department of Mathematics of KU-Leuven How to get to our department Research Unit Algebraic Geometry and Number Theory of KU-Leuven Leuven-Gent Seminar on Number Theory and Algebraic Geometry Math Database 1931-1999 Mathematics Information Servers Algebraic Geometry Preprint Server European Singularities Network Number Theory Preprint Server Algebraic Number Theory Archives MSRI Mathematical Sciences Research Institute American Mathematical Society Back to top
Daniel, Stephan
University of Cardiff. Analytic number theory. Publications.
Stephan Daniel's Homepage Stephan Daniel's Homepage HOME Publications Current position: Post-doctoral fellow, funded by EPSRC, at the School of Mathematics of the University of Wales in Cardiff. Address: Dr. Stephan Daniel SchoolofMathematics Cardiff University P.O. Box 926 Cardiff CF24 4YH - Wales, U.K. - Phone: (++44) (0)29 2087 6862 Fax: (++44) (0)29 2087 4199 Email: DanielS1@cf.ac.uk Cardiff University School of Mathematics EPSRC Last modified 18 3 2000 by sd
Damianou, Pantelis
University of Cyprus. Lie Groups; Integrable Systems; Poisson Geometry; Number Theory. Publications, talks.
Pantelis Damianou - Department of Mathematics and Statistics - Univertity of Cyprus I received a Masters degree in Mathematics from UCLA in 1980 and a Ph.D. from the University of Arizona in 1989. I have a B.Sc. degree from the University of New Hampshire in 1977. I worked as an actuary for Farmers Insurance group in Los Angeles between my Masters and Ph.D. I was an Assistant Professor at the Department of Mathematics at University of Arizona for two years. I then joined the Department of Mathematics and Statistics at the University of Cyprus in 1992. PANTELIS A. DAMIANOU Professor Research Interests Education Email: damianou@ucy.ac.cy Phone: +357 22 892654 Fax: +357 22 892601 Department of Mathematics and Statistics University of Cyprus P. O. Box 20537 1678, Nicosia, Cyprus Lie Groups Integrable Systems Poisson Geometry Number Theory 1985-1989 University of Arizona Ph.D. Mathematics, May 1989. Thesis advisor: Hermann Flaschka 1978-1981 UCLA M.A. Mathematics, March 1980. 1974-1977 University of New Hampshire B.S. Mathematics, May 1977. More ... Employment History Administration Reviews-Editorial Boards Courses Taught Students Supervised MAS223 Conferences, Visits, Talks Publications Photos Curriculum Vitae (pdf) (ps)
Dorman, David R.
Middlebury College. Algebraic Number Theory and Arithmetical Algebraic Geometry. Contact information.
David R. Dorman's Home Page David R. Dorman I graduated from the Department of Mathematics at Brown University. My main areas of interest are Algebraic Number Theory and Arithmetical Algebraic Geometry. I am currently a professor at Middlebury College. Some Favorite Links Yahoo the super big WWW directory dorman@panther.middlebury.edu
Dokchitser, Tim
University of Durham. Arithmetic algebraic geometry. Publications, thesis, Pari GP software.
Tim Dokchitser's home page DPMMS Robinson Maths ComputeL Search Tim Dokchitser Robinson College, Cambridge, CB3 9AN tel. 01223 339141 Dept of Pure Maths and Math Statistics Centre for Mathematical Sciences University of Cambridge Wilberforce Road, Cambridge, CB3 0WB tel. 01223 765818 DPMMS office C0.11 Mathematics My Ph.D. thesis (2000, University of Utrecht, The Netherlands) is ``Deformations of p-divisible groups and p-descent on elliptic curves'' This is a link to the thesis , and on the right is a link to the genealogy tree of my Ph.D. ancestors (light) and some of my Ph.D. relatives (dark). Most of the data comes fromthe Mathematics Genealogy Project at Minnesota State University. My Ph.D. genealogy tree Recent publications preprints: Computing special values of motivic L-functions, Exp. Math. 13, No.2, 137-149 (2004) ( arxiv ) LLL ABC, J. Number theory 107, No.1, 161-167 (2004) ( arxiv ) for the additional ABC examples see the ABC conjecture home page Numerical verification of Beilinson's conjecture for K2 of hyperelliptic curves, with R. de Jeu and D. Zagier, to appear in Compositio Math. ( arxiv ) Computations in non-commmutative Iwasawa theory, with V. Dokchitser (appendix by J. Coates and R. Sujatha) ( arxiv ) On the 6-colour conjecture in R3, with V. Dokchitser ( ps ) Ranks of elliptic curves in cubic extensions ( arxiv ) Quotients of functors of Artin rings ( arxiv ) Most of my work concerns the "standard conjectures" for L-functions associated to arithmetic varieties. I have implemented algorithms to compute special values of these L-functions in Pari ( ComputeL ) and in Magma (starting from V2.12, July 2005, handbook ). Search the web General search engines Altavista Any language English Dutch German Russian Google advanced Yahoo Cambridge Second hand books AddAll by title advanced AddAll by author advanced Amazon All Products Books Popular Music Electronics Software Auctions zShops BestBookBuys Title Author Keyword ISBN New books Amazon All Products Books Popular Music Electronics Software Auctions zShops Bookshop (UK) advanced Mathematics Integer sequence MathSciNet Author Related Author Title Review Text Journal Institution Code Series MSC Prim. Sec. MSC Primary MR Number Reviewer Anywhere Ref Author Ref Anywhere Other Movies (IMDB) All Titles My Movies People Characters Quotes Bios Plots
Duquesne, Sylvain
Universit Montpellier II. Arithmetic and algorithmic number theory and applications in cryptography; arithmetic of curves of genus 2 or higher. Publications, software.
Sylvain Duquesne's home page
Duke, William
University of California Los Angeles. Number theory and automorphic forms. Publications.
Home page of William Duke William Duke Professor of Mathematics, UCLA e-mail : wdduke at ucla dot edu Phone: 310-825-1652 Fax: 310-206-6673 Mailing address: UCLA Mathematics Department Box 951555, Los Angeles, CA 90095-1555 Office: 6939 Math Sciences Building, UCLA Math Reviews (You must have a subscription to view) Papers by W. Duke Preprints (in PDF) Special values of multiple gamma functions, with O. Imamoglu, to appear in J. de Thorie des Nombres de Bordeaux Modular functions and the uniform distribution of CM points, to appear in Math. Ann. Preprint Versions of Recent Papers (in PDF) Continued fractions and modular functions , Bull. Amer. Math. Soc. (N.S.) 42 (2005), no. 2, 137--162 Quadratic reciprocity in a finite group, with K. Hopkins, Amer. Math. Monthly 112 (2005), no. 3, 251--256. On ternary quadratic forms , J. Number Theory 110 (2005), no. 1, 37--43. Lattice points in cones and Dirichlet series, with O. Imamoglu, IMRN 53 (2004) Number fields with large class groups , in Number Theory, CNTA VII, CRM Proceedings, 2004 Reductions of an elliptic curve and their Tate-Shafarevich groups , with A. Cojocaru, Math. Annalen 329, 513-534 (2004) Extreme values of Artin L-functions and class numbers , Compositio Math. 136, 103-115 (2003) Almost all reductions of an elliptic curve have a large exponent , Comptes Rendus. 337 11, 689-692 (2003) Rational points on the sphere , The Ramanujan Journal 7 , 235-239 (2003) The splitting of primes in division fields of elliptic curves , with A. Toth, Experimental Math. 11,555-565 (2003) Grad Students (PhD Year) Current John Leo Amanda Folsom (2006) Previous Nathan Jones (2005) Ryan Daileda (2004) Arpad Toth (1997) Courses Current Fall 2005 246B Recent Spring 2005 246A Links The Gauss-Dirichlet conference (2005) The Number Theory Group at UCLA UCLA math department home page
Doche, Christophe
Macquarie University, Sydney. Analytic and algorithmic number theory: Mahler measure and Lehmer's problem; Rudin-Shapiro polynomials. Publications, thesis, Pari GP code.
Christophe Doche's home page This page is no longer maintained Click here to be redirected to my new homepage Version franaise CHRISTOPHE DOCHE Lecturer l'universit de Macquarie (Sydney) Division of ICS Building E6A Office 376 Macquarie University NSW 2109 Australia Phone: (+61) 2 9850 9576 Fax: (+61) 2 9850 9551 email: doche_at_ics.mq.edu.au Curriculum vitae Research Collective activities Talks Teaching Links Curriculum vitae Born June 25, 1971 in Bordeaux. Degrees: Baccalaurat C (Bordeaux, 1989) Deug de Droit (University Bordeaux I, 1992) Deug A (University Bordeaux I, 1993) Licence de Mathmatiques Pures (University Bordeaux I, 1994) Matrise de Mathmatiques Pures (University Bordeaux I, 1995) DEA de Mathmatiques Pures (University Bordeaux I, 1996) Agrgation de Mathmatiques (option Mathmatiques pour l'Informatique, 1996) Doctorat de Mathmatiques Pures (University Bordeaux I, 2000) Positions: Ph.D. student from 1997 to 2000. Moniteur at the University Bordeaux I from 1998 to 2000 (lectures at the IUT A of Bordeaux). A.T.E.R. at the University Bordeaux I from 2000 to 2001. Cryptograher for the AREHCC project from 2001 to 2003. Lecturer at Macquarie University from 2003. Research I obtained a D.E.A. (master) in number theory at the University Bordeaux I in 1996, supervised by Michel Langevin. My report entitled Problme de Lehmer, nombres de Pisot et de Salem au fil des travaux de Boyd, can be found here: dea.ps.gz (zipped postscript format. Using Windows you will need gzip.exe and ghostview to view this file). I defended my thesis entitled Mesures de Mahler et racines relles de certaines familles de polynmes on June 21, 2000 at the University Bordeaux I [ these.ps.gz ]. My Ph.D. advisors were Laurent Habsieger and Michel Langevin. I am interested in analytic number theory and algorithmic. For example, you can get a file of routines PARI [ mahler.gp ] to compute particularly Mahler measures of polynomials in one and two variables. More specifically I am working on Lehmer's problem and on the determination of the number of real zeros of certain families of polynomials with coefficients plus or minus 1, e.g. Thue-Morse polynomials. I explore also another topic with Laurent Habsieger , namely the Rudin-Shapiro polynomials and more precisely the moments of order q of these polynomials. The only result previously known, due to Littlewood, gives the recurrence satisfied by these moments for q=4. We were able to determine explicitly similar linear recurrences for all the even moments q between 4 and 32. Furthermore if L is the length of the Rudin-Shapiro polynomial of order n, that is the sum of the absolute value of its coefficients i.e. L=2^n, we showed that the asymptotic behaviour of these moments was (2L)^(q 2) (q 2+1) for all even q less than or equal to 52. This result was expected and conjectured by Saffari. We try to extend this work to all q and to generalized Rudin-Shapiro polynomials. Finally I am doing research on efficiency aspects of cryptosystems based on elliptic and hyperelliptic curves defined over finite fields. My list of papers can be found below: On the Zhang Zagier height: On the spectrum of the Zhang-Zagier height, Math. Comp . 70 (2001), no. 233, 419-430. [ spectrum.ps.gz ] Zhang-Zagier heights of perturbed polynomials, Journal de Thorie des Nombres de Bordeaux 13 (2001), 103-110, proceedings des XXIe Journes Arithmtiques. [ perturbed.ps.gz ] Sur les zros rels des polynmes : On the real roots of generalized Thue-Morse polynomials, Acta Arith. XCIX.4 (2001), 309-319. [ genethuemorse.ps.gz ] Integral Geometry and real zeros of Thue-Morse polynomials, with Michel Mends France, Experiment. Math. 9 (2000), no. 3, 339-350. [ thuemorse.ps.gz ] Real roots! with Michel Mends France, Analytic and probabilistic methods in number theory (Palanga), TEV, Vilnius 2002. [ realroots.ps.gz ] An exercise on the average number of real zeros of random real polynomials with Michel Mends France, Finite and infinite combinatorics (Budapest 2001). J. Bolyai Mathematical Society. [ finf.ps.gz ] On the moments of the Rudin-Shapiro polynomials : Moments of the Rudin-Shapiro Polynomials, with Laurent Habsieger, to appear in the Journal of Fourier Analysis and Applications. [ 049.ps.gz ] Even moments of generalized Rudin--Shapiro polynomials, submitted to Math. Comp. [ genersmc.ps.gz ] A gp program to precisely compute the moments of the Rudin-Shapiro polynomial of order q even less than or equal to 32 and the moments of some generalized Rudin-Shapiro polynomials is available here [ moments.gp.gz ] as well as the tables of minimal polynomials for the recurrences and the first moments [ data.gz ] et [ data32.gz ] On an efficient implementation of finite fields in characteristic 2: Redundant Trinomials for Finite Fields of Characteristic 2, preprint. [redundant.ps.gz] A table of redundant polynomials written in gp is also available. Collective activities Organizer with Jean-Jacques Ruch of the Sminaire de Thorie Analytique des Nombres de Bordeaux since 1999. Organizer with Jean-Paul Allouche and Jean-Jacques Ruch of the Colloque en l'honneur de Michel Mends France from September 11 to 14, 2000 in Bordeaux. Talks On the spectrum of the Zhang-Zagier height: Groupe de Travail de Thorie Analytique des Nombres , Avril 1998, Bordeaux. Colloque Jeunes Chercheurs, September 1998, Caen. Groupe d'Etude des Problmes Diophantiens, December 1998, Paris. Sminaire de Thorie des Nombres,