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Top: Science: Math: Number_Theory: Elliptic_Curves_and_Modular_Forms:

Elliptic Curves and Modular Forms

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» 14H52: Elliptic Curves - From the Known Math series. » 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. » Algorithms for Modular Elliptic Curves - Book by John Cremona, with introduction, tables and software. » An Elementary Introduction to Elliptic Curves - By Len Charlap, David Robbins and Raymond Coley. Downloadable text in PostScript (.ps) format. » Arithmetic of Cuves - Papers and surveys by Ed Schaefer. » Bibliography for Automorphic and Modular Forms, L-Functions, Representations, and Number Theory - Compiled by Paul Garrett, 1996. » 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 by to Takakazu Satoh. » Course Notes - Full notes as .dvi, .pdf, and .ps files for all the advanced courses J. S. Milne taught between 1986 and 1999. » ECDL Project - Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers. » ECMNET - The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers. » Elliptic Curves - Links to research papers maintained by Stéfane Fermigier. » Elliptic Curves Handout - Syllabus and detailed reading list by Miles Reid, University of Warwick. » Elliptic Curves II - Lecture notes by Johan P. Hansen. » Elliptic Curves and Cryptology - Marc Joye's list of elliptic curve resources includes people, books, and links. Many preprints are available from the site. » Elliptic Curves and Elliptic Functions - Introductory notes by Charles Daney. » Elliptic Curves and Formal Groups - Lecture notes from a seminar J. Lubin, J.-P. Serre and J. Tate. » Elliptic Curves and Right Triangles - Slides (GIF) of lectures by Karl Rubin at Stanford University. » Elliptic Curves and Their Applications to Cryptography - Web text by Andreas Enge. » Elliptic Curves with H. A. Verrill - Lecture notes and resources by Helena Verrill, Louisiana State University, 2004. » Elliptic Divisibility Sequences - Articles and links, compiled by Graham Everest. » Elliptic Functions and Elliptic Curves - Lecture notes by Jan Nekovář (PS/PDF). » Elliptical Curve Cryptography - Explains the difference between an elliptical curve and an ellipse. Discusses fields, applications, choosing a fixed point, and related topics. » Explicit Approaches to Modular Abelian Varieties - William Stein, Ph.D. thesis, Berkeley, 2000. » History of Elliptic Curve Rank Records - A table up to rank 24 compiled by Andrej Dujella. » Iwasawa Theory of Elliptic Curves - Lecture notes and surveys by Ralph Greenberg, University of Washington (PS). » Joseph Silverman - Includes errata for his books Rational Points on Elliptic Curves and Advanced Topics in the Arithmetic of Elliptic Curves. » 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. » 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. » Modular Forms Course - Notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators. » Modular Forms and Hecke Operators - Notes by William A. Stein of a course by Ken Ribet. » Monstrous Moonshine - the surprising and mysterious connections between the monster (and also other finite sporadic simple groups) and modular functions. » Moonshine Bibliography - Books and papers relating to the Conway-Norton-Thompson Moonshine conjecture, proved by Richard Borcherds. » On 5 and 7 Descents for Elliptic Curves - Tom Fisher's Ph.D. thesis (Cambridge, 2000) in DVI and PS format. » Papers by Richard Borcherds - Including proof of the Moonshine Conjecture (TeX,DVI,PDF). » Prime Values of Elliptic Divisibility Sequences - By Graham Everest. » Rational Points on Elliptic Curves - A course by Jerrold Tunnell. An introduction to rational points on elliptic curves through examples. » 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. » Richard Taylor - Publications including the joint paper with Andrew Wiles which completed the proof of Fermat's Last Theorem. » 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.

Last Updated: 2007-02-20 09:05:04