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Topia!: Science: Math: Number Theory: Elliptic Curves and Modular Forms (68)
See Also:
Elliptic Curves and Formal Groups - Lecture notes from a seminar J. Lubin, J.-P. Serre and J. Tate. Joseph Silverman - Includes errata for his books Rational Points on Elliptic Curves and Advanced Topics in the Arithmetic of Elliptic Curves. ECMNET - The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers. Course Notes - Full notes as .dvi, .pdf, and .ps files for all the advanced courses J. S. Milne taught between 1986 and 1999. Publications of François Morain - Thesis and papers on elliptic curves, especially primality proofs and point counting. Elliptic Curves and Cryptology - Marc Joye's list of elliptic curve resources includes people, books, and links. Many preprints are available from the site. Mathematical Things - 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. ECDL Project - Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers. Counting Points on Elliptic Curves - Robert Harley, Pierrick Gaudry, François Morain and Mireille Fouquet have established new records for point counting in characteristic 2, using a new algorithm due to Takakazu Satoh. David Pollack - The author's thesis "Explicit Hecke Actions on Modular Forms, Harvard, 1998" is available here in DVI form. Modular Curves X_0(N) - A series of lectures by Bas Edixhoven at the ICTP Summer school on rational torsion of elliptic curves over number fields. Elliptic Curves II - Lecture notes by Johan P. Hansen. Rational Points on Elliptic Curves - A course by Jerrold Tunnell. An introduction to rational points on elliptic curves through examples. Elliptic Curves and Right Triangles - Slides (GIF) of lectures by Karl Rubin at Stanford University. Papers by Richard Borcherds - Including proof of the Moonshine Conjecture (TeX,DVI,PDF). Satoh-FGH algorithm - Gonzalez and Harley explain Professor Satoh's elliptic curve point counting algorithm. Elliptic Curves Handout - Syllabus and detailed reading list by Miles Reid, University of Warwick. 14H52: Elliptic Curves - From the Known Math series. Algorithms for Modular Elliptic Curves - Book by John Cremona, with introduction, tables and software. Modular Forms Example Sheets - From a course on modular forms. Kolyvagin Seminar - A semester-long seminar studying Kolyvagin's application of Euler systems to elliptic curves. Includes extensive lecture notes in PostScript or DVI format. A Proof of the Full Shimura-Taniyama-Weil Conjecture - PDF-format article by Henri Darmon on the completion of the proof by Wiles, Breuil, Conrad, Diamond and Taylor. Monstrous Moonshine - the surprising and mysterious connections between the monster (and also other finite sporadic simple groups) and modular functions. Modularity of Elliptic Curves and Beyond - Workshop, MSRI Berkeley, 6-10 December 1999. Recent Progress in the Theory of Elliptic Curves - 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. Bibliography for Automorphic and Modular Forms, L-Functions, Representations, and Number Theory - Compiled by Paul Garrett, 1996. Prime Values of Elliptic Divisibility Sequences - By Graham Everest. Modular Forms Course - Notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators. Elliptic Divisibility Sequences - Articles and links, compiled by Graham Everest. Explicit Approaches to Modular Abelian Varieties - William Stein, Ph.D. thesis, Berkeley, 2000. Elliptic Curves and Elliptic Functions - Introductory notes by Charles Daney. Moonshine Bibliography - Books and papers relating to the Conway-Norton-Thompson Moonshine conjecture, proved by Richard Borcherds. Iwasawa Theory of Elliptic Curves - Lecture notes and surveys by Ralph Greenberg, University of Washington (PS). Douglas Ulmer's Publications and Preprints - Mainly on elliptic curves and modular forms. Matt Baker's Papers - Mainly on elliptic curves. On 5 and 7 Descents for Elliptic Curves - Tom Fisher's Ph.D. thesis (Cambridge, 2000) in DVI and PS format. Modular Forms and Hecke Operators - Notes by William A. Stein of a course by Ken Ribet. Richard Taylor - Publications including the joint paper with Andrew Wiles which completed the proof of Fermat's Last Theorem. Arithmetic of Cuves - Papers and surveys by Ed Schaefer. An Elementary Introduction to Elliptic Curves - By Len Charlap, David Robbins and Raymond Coley. Downloadable text in PostScript (.ps) format. The Birch and Swinnerton-Dyer Conjecture - A Clay Mathematics Institute Prize problem, with description by Andrew Wiles [PDF] and lecture by Fernando Rodriguez-Villegas [.ram]. Torsion Points on Elliptic Curves - Elementary introduction and brief explanation of some well-known results.
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