Top > Science > Math > Number Theory > Elliptic Curves and Modular Forms

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• Science: Math: Number Theory: Diophantine Equations: Fermat's Last Theorem  (15)
• Science: Math: Number Theory: Factoring  (53)
• Science: Math: Number Theory: Prime Numbers: Primality Tests: Primality Proving  (12)

» 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.

» 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].

» 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.

» An Elementary Introduction to Elliptic Curves - By Len Charlap, David Robbins and Raymond Coley. Downloadable text in PostScript (.ps) format.

» Elliptic Curves - Links to research papers maintained by Stéfane Fermigier.

» 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 Handout - Syllabus and detailed reading list by Miles Reid, University of Warwick.

» Elliptic Curves II - Lecture notes by Johan P. Hansen.

» 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.

» 14H52: Elliptic Curves - From the Known Math series.

» 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 and Hecke Operators - Notes by William A. Stein of a course by Ken Ribet.

» Modular Forms Course - Notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators.

» 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.

» A Proof of the Full Shimura-Taniyama-Weil Conjecture - Article by Henri Darmon on the completion of the proof by Wiles, Breuil, Conrad, Diamond and Taylor. [PDF]

» 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.

» Torsion Points on Elliptic Curves - Elementary introduction and brief explanation of some well-known results.

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