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Search Home : Science : Math : Number Theory : Elliptic Curves and Modular Forms
See Also:
- 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 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.
- Matt Baker's Papers: Mainly on elliptic curves.
- 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.
- Modular Forms Course: Notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators.
- Modular Forms Example Sheets: From a course on modular forms.
- Modular Forms and Hecke Operators: Notes by William A. Stein of a course by Ken Ribet.
- Modularity of Elliptic Curves and Beyond: Workshop, MSRI Berkeley, 6-10 December 1999.
- 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.
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