Elliptic Curves and Modular Forms Number Theory Math
Elliptic Curves and Modular Forms Number Theory Math
Elliptic Curves are related to the solutions to equations y^2 = x^3 + A x + B in the field of rationals, algebraic extensions of the rationals, p-adic rational numbers, or a finite field. They are used in factorization of integers and also played a role in the recent resolution of the conjecture known as Fermat's Last Theorem.
Top: Science: Math: Number Theory: Elliptic Curves and Modular Forms
See Also:
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Elliptic Curves and Formal Groups - Lecture notes from a seminar J. Lubin, J.-P. Serre and J. Tate.
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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.
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Course Notes - Full notes as .dvi, .pdf, and .ps files for all the advanced courses J. S. Milne taught between 1986 and 1999.
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Arithmetic of Cuves - Papers and surveys by Ed Schaefer.
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Elliptic Functions and Elliptic Curves - Lecture notes by Jan Nekovář (PS/PDF).
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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]
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Elliptic Curves and Their Applications to Cryptography - Web text by Andreas Enge.
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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.
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Joseph Silverman - Includes errata for his books Rational Points on Elliptic Curves and Advanced Topics in the Arithmetic of Elliptic Curves.
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Richard Taylor - Publications including the joint paper with Andrew Wiles which completed the proof of Fermat's Last Theorem.
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An Elementary Introduction to Elliptic Curves - By Len Charlap, David Robbins and Raymond Coley. Downloadable text in PostScript (.ps) format.
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Explicit Approaches to Modular Abelian Varieties - William Stein, Ph.D. thesis, Berkeley, 2000.
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Elliptic Curves and Cryptology - Marc Joye's list of elliptic curve resources includes people, books, and links. Many preprints are available from the site.
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14H52: Elliptic Curves - From the Known Math series.
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Rational Points on Elliptic Curves - A course by Jerrold Tunnell. An introduction to rational points on elliptic curves through examples.
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Bibliography for Automorphic and Modular Forms, L-Functions, Representations, and Number Theory - Compiled by Paul Garrett, 1996.
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History of Elliptic Curve Rank Records - A table up to rank 24 compiled by Andrej Dujella.
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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].
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Iwasawa Theory of Elliptic Curves - Lecture notes and surveys by Ralph Greenberg, University of Washington (PS).
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Elliptic Curves and Elliptic Functions - Introductory notes by Charles Daney.
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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.
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Elliptic Curves Handout - Syllabus and detailed reading list by Miles Reid, University of Warwick.
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ECMNET - The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers.
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ECDL Project - Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers.
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Prime Values of Elliptic Divisibility Sequences - By Graham Everest.
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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.
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On 5 and 7 Descents for Elliptic Curves - Tom Fisher's Ph.D. thesis (Cambridge, 2000) in DVI and PS format.
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Elliptic Curves with H. A. Verrill - Lecture notes and resources by Helena Verrill, Louisiana State University, 2004.
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Elliptic Divisibility Sequences - Articles and links, compiled by Graham Everest.
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Elliptical Curve Cryptography - 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 Curves II - Lecture notes by Johan P. Hansen.
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Modular Forms Course - Notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators.
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Modular Forms and Hecke Operators - Notes by William A. Stein of a course by Ken Ribet.
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Torsion Points on Elliptic Curves - Elementary introduction and brief explanation of some well-known results.
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Elliptic Curves - Links to research papers maintained by Stéfane Fermigier.
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Elliptic Curves and Right Triangles - Slides (GIF) of lectures by Karl Rubin at Stanford University.
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Papers by Richard Borcherds - Including proof of the Moonshine Conjecture (TeX,DVI,PDF).
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