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Elliptic Curves and Modular Forms
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Links to research papers maintained by Stéfane Fermigier.
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Elliptic curves This page is a collection of links on research articles on elliptic curves and related topics (applications, modular forms, FLT Introduction. Introduction élémentaire la théorie des courbes elliptiques (Marc Joye Draft chapters 1,2 of elliptic curve handbook ECH1 Ian Connell...Lecture notes from a seminar J. Lubin, J.-P. Serre and J. Tate.
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Elliptic curves and formal groups Elliptic curves and formal groups by J. Lubin, J.-P. Serre and J. Tate This page contains scanned copies of the lecture notes of the seminar run by J. Lubin, J.-P. Serre and J. Tate, which is part of the Lecture...Tom Womack's pages address many elliptic curve subjects, including curves of given rank and small conductor, Mordell curves of large rank, and interesting torsion groups.
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Mathematical Things I said on the previous page, I'm a second-year post-graduate mathematician at the University of Nottingham, supervised by John Cremona, and working on computational number theory, concentrating on extending the well-known and effective algorithms for computing the ranks of elliptic...Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers.
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ECDL Project Here are two papers about counting points: on elliptic curves and on hyperelliptic curves. INRIA, Domaine de Voluceau Rocquencourt, 78153 Le Chesnay, France. Please note: These pages are no longer maintained (since circa December 2000...Lecture notes by Johan P. Hansen.
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Ell-E99.html The course is a continuation of the spring course: Elliptic curves over Q and C and will treat modular forms and elliptic curves. Prerequisites: Elliptic Curves, Chap. I-IV. Literature: Anthony W. Knapp: Elliptic Curves, Princeton University Press Jean-Pierre Serre: A...A course by Jerrold Tunnell. An introduction to rational points on elliptic curves through examples.
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Mathematics 574 (Fall 2004) Information Information concerning the course Mathematics 574 (Selected Topics in Number Theory) to be taught in Fall 2004 by J. Tunnell is kept here. The course will be an introduction to rational points on elliptic curves through examples of interesting elliptic...Slides (GIF) of lectures by Karl Rubin at Stanford University.
http://math.stanford.EDU/~rubin/lectures/sumo/
Syllabus and detailed reading list by Miles Reid, University of Warwick.
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MA426 Elliptic curves This directory contains information for the course MA 426 on Elliptic curves, that I gave as a lecture course in 1999, 2000, as a reading course in 2001-2004, and that Samir Siksek is offering in 2005. The 45 page handout...From the Known Math series.
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14H52: Elliptic Curves This is a fascinating area of algebraic geometry dealing with nonsingular curves of genus 1 in English, solutions to equations y^2 x^3 A x B. It turns out to have important connections to number theory and in particular to factorization...Book by John Cremona, with introduction, tables and software.
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ALGORITHMS FOR MODULAR ELLIPTIC CURVES: INTRODUCTION This book is in three sections. First, we describe in detail an algorithm based on modular symbols for computing modular elliptic curves: that is, one-dimensional factors of the Jacobian of the modular curve $X_0(N which are attached to certain cusp...From a course on modular forms.
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Modular forms example sheets These are tex files of some example sheets for a modular forms course. The files may have been compressed with gzip, in which case they can be uncompressed using the command gunzip. Example sheet 1 Example sheet 2. Example sheet...PDF-format article by Henri Darmon on the completion of the proof by Wiles, Breuil, Conrad, Diamond and Taylor.
http://www.ams.org/notices/199911/comm-darmon.pdf
the surprising and mysterious connections between the monster (and also other finite sporadic simple groups) and modular functions.
http://cicma.concordia.ca/faculty/cummins/moonshine.html
Workshop, MSRI Berkeley, 6-10 December 1999.
http://www.msri.org/activities/events/9900/hottopics/
An abstract to Henri Darmon's and Bertolini's work, which approaches a p-adic variant of the Birch - Swinnerton-Dyer conjecture, for curves of rank higher than one.
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Henri Darmon Recent progress in the theory of elliptic curves S media releases search site map membership and publications membership publications website accounts activities competitions grants math camps meetings past meetings prizes awards resources education employment research students women links other links other societies Next: DOCTORAL PRIZE LECTURE Up: COXETER-JAMES...Compiled by Paul Garrett, 1996.
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bibliography for automorphic and modular forms, L-functions, representations, and number theory Bibliography for automorphic and modular forms, L-functions, and representation theory Last updated 1996 Also see the much newer specialized bibliography for Buildings, Classical Groups, and Representations of p-adic Groups The following biblography was compiled for my students. It is not...By Graham Everest.
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Prof Graham R Everest, MTH, UEA Chudnovsky considered some EDSs specified by writing down their first five terms and examined these sequences for prime terms. Since u[n] is a divisibility sequence, which grows so quickly, it is sufficient to examine prime occurence of terms u[n] with...Notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators.
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William Stein Talks Boston see also source code. Tamagawa Numbers and Visibility (November AMS meeting in Pittsburgh) An Introduction to the Birch and Swinnerton-Dyer Conjecture (Nov at UW in Seattle) Visibility of Shafarevich-Tate Groups at Higher Level Oct at UT Austin, Nov at...Articles and links, compiled by Graham Everest.
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Prof Graham R Everest, MTH, UEA This means all the terms are integers and u[n] divides u[m] whenever n divides m. The sequence is said to be an Elliptic Divisibility Sequence (hereafter EDS) if it satisfies the recurrence relation u[m-n]u[m+n u[m+1]u[m-1]u[n]2 u[n+1]u[n-1]u[m]2 for all m n...William Stein, Ph.D. thesis, Berkeley, 2000.
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William Stein's Ph.D. thesis Explicit approaches to modular abelian varieties William Arthur Stein Doctor of Philosophy in Mathematics University of California at Berkeley Professor Hendrik Lenstra, Chair Spring 2000 I investigate the Birch and Swinnerton-Dyer conjecture, which ties together the constellation of invariants attached...Introductory notes by Charles Daney.
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Elliptic Curves and Elliptic Functions For a quick definition of many of the terms used here, you may refer to the Glossary. Contents: What is an elliptic curve? The group structure of an elliptic curve Arithmetic on elliptic curves Further basic concepts and results What...Books and papers relating to the Conway-Norton-Thompson Moonshine conjecture, proved by Richard Borcherds.
http://cicma.concordia.ca/faculty/cummins/moonshine.refs.html
Lecture notes and surveys by Ralph Greenberg, University of Washington (PS).
http://www.math.washington.edu/~greenber/research.html
Tom Fisher's Ph.D. thesis (Cambridge, 2000) in DVI and PS format.
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Tom Fisher's Home Page Thesis A dissertation submitted for the degree of Doctor of Philosophy at the University of Cambridge, August 2000 Abstract We perform descent calculations for the families of elliptic curves over Q with a rational point of order n 5 or 7....Notes by William A. Stein of a course by Ken Ribet.
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Modular Forms Course The version here is the original very rough form. Though they flow well, they contain all kinds of inaccuracies and are annoyingly incomplete. Thus at present I definitely wouldn't recommend them for study. However, I've been rewriting and extending them...Publications including the joint paper with Andrew Wiles which completed the proof of Fermat's Last Theorem.
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Richard Taylor's Home Page 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....Papers and surveys by Ed Schaefer.
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Things of interest to number theorists Here is a list of my papers followed by postscript files of eight lectures. 2-descent on the Jacobians of hyperelliptic curves, Journal of Number Theory 51 1995, 219-232. Class groups and Selmer groups, Journal of Number Theory 56 1996, 79-114....By Len Charlap, David Robbins and Raymond Coley. Downloadable text in PostScript (.ps) format.
http://www.idaccr.org/reports/reports.html
Elementary introduction and brief explanation of some well-known results.
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Torsion points on elliptic curves Torsion points on elliptic curves Xavier Xarles The main object of arithmetic geometry is to find all the solutions of Diophantine equations. Examples: Find all the rational numbers X and Y such that X2 Y2 1 Find all the rational...A table up to rank 24 compiled by Andrej Dujella.
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History of elliptic curves rank records History of elliptic curves rank records Let E be an elliptic curve over Q. By Mordell's theorem, E(Q) is a finitely generated abelian group. This means that E(Q E(Q)tors × Zr. By Mazur's theorem, we know that E(Q)tors is one...Explains the difference between an elliptical curve and an ellipse. Discusses fields, applications, choosing a fixed point, and related topics.
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Elliptic curve cryptography FAQ v1.12 22nd December 1997 Elliptic curve cryptography FAQ v1.12 22nd December 1997 by George Barwood (1) What is an elliptic curve? Well for a start, it is not the same as an ellipse! But to be more positive: from school mathematics, you probably know...Web text by Andreas Enge.
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Elliptic Curves and Their Applications to Cryptography: An Introduction Next: Contents Elliptic Curves and Their Applications to Cryptography: An Introduction Andreas Enge Date: September 1999 Contents Foreword Preface Public Key Cryptography The Group Law on Elliptic Curves Elliptic Curves over Finite Fields The Discrete Logarithm Problem Counting Points on...Robert Harley, Pierrick Gaudry, François Morain and Mireille Fouquet have established new records for point counting in characteristic 2, using a new algorithm by to Takakazu Satoh.
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Counting points on elliptic curves Counting points on elliptic curves Counting points on elliptic curves One of the topics of my PhD research is point counting on elliptic curves using the new algorithm due to Takakazu Satoh. My colleagues Robert Harley, Pierrick Gaudry and François...A Clay Mathematics Institute Prize problem, with description by Andrew Wiles [PDF] and lecture by Fernando Rodriguez-Villegas [.ram].
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Clay Mathematics Institute Dedicated to increasing and disseminating mathematical knowledge HOME| ABOUT CMI| PROGRAMS| NEWS EVENTS| AWARDS| SCHOLARS| PUBLICATIONS Birch and Swinnerton-Dyer Conjecture Mathematicians have always been fascinated by the problem of describing all solutions in whole numbers x,y,z to algebraic equations like...Lecture notes by Jan Nekovář (PS/PDF).
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DEA 2003/04 Elliptic functions and elliptic curves I. Analytic theory postscript (version 20/9/2004) pdf (version 20/9/2004) II. Algebraic theory postscript (version 5/2/2004) pdf (version 5/2/2004) Licence agreement: You can download these notes for free. If you like the notes, then if you...A semester-long seminar studying Kolyvagin's application of Euler systems to elliptic curves. Includes extensive lecture notes in PostScript or DVI format.
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GraNTS If you are looking for the web page of last Spring's Kolyvagin seminar, you want here instead. Practical information Seminar description Lecture notes Lecture schedule References Practical Information Organizers: Alex Ghitza (aghitza@math.mit.edu) and Brian Osserman (osserman@math.mit.edu) When: Fall 2000, 2...Lecture notes and resources by Helena Verrill, Louisiana State University, 2004.
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Elliptic curves with H. A. Verrill We will stick pretty closely to the text. Assessment: will be on about 4 or 5 homeworks (taken from exercises in the book plus students should give a talk at the very end on some aspect of elliptic curves, e.g...