Elliptic Curves and Modular Forms (Number Theory)

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Arithmetic of Cuves Arithmetic of Cuves: Papers and surveys by Ed Schaefer. (Elliptic Curves and Modular Forms) http://math.scu.edu/~eschaefe/nt.html Moonshine Bibliography Moonshine Bibliography: Books and papers relating to the Conway-Norton-Thompson Moonshine conjecture, proved by Richard Borcherds. (Elliptic Curves and Modular Forms) http://cicma.concordia.ca/faculty/cummins/moonshine.refs.html Elliptic Curves and Cryptology 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 Modular Forms) http://www.geocities.com/marcjoye/biblio_ell.html Elliptic Curves Handout Elliptic Curves Handout: Syllabus and detailed reading list by Miles Reid, University of Warwick. (Elliptic Curves and Modular Forms) http://www.maths.warwick.ac.uk/~miles/MA426/ Course Notes Course Notes: Full notes as .dvi, .pdf, and .ps files for all the advanced courses J. S. Milne taught between 1986 and 1999. (Elliptic Curves and Modular Forms) http://www.jmilne.org/math/CourseNotes/ Explicit Approaches to Modular Abelian Varieties Explicit Approaches to Modular Abelian Varieties: William Stein, Ph.D. thesis, Berkeley, 2000. (Elliptic Curves and Modular Forms) http://modular.fas.harvard.edu/papers/explicit/ Elliptic Curves and Elliptic Functions Elliptic Curves and Elliptic Functions: Introductory notes by Charles Daney. (Elliptic Curves and Modular Forms) http://cgd.best.vwh.net/home/flt/flt03.htm 14H52: Elliptic Curves 14H52: Elliptic Curves: From the Known Math series. (Elliptic Curves and Modular Forms) http://www.math.niu.edu/~rusin/known-math/index/14H52.html Recent Progress in the Theory of Elliptic Curves 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. (Elliptic Curves and Modular Forms) http://www.cms.math.ca/CMS/Events/winter98/w98-abs/node2.html ECMNET ECMNET: The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers. (Elliptic Curves and Modular Forms) http://www.loria.fr/~zimmerma/records/ecmnet.html Joseph Silverman Joseph Silverman: Includes errata for his books Rational Points on Elliptic Curves and Advanced Topics in the Arithmetic of Elliptic Curves. (Elliptic Curves and Modular Forms) http://www.math.brown.edu/~jhs/ Algorithms for Modular Elliptic Curves Algorithms for Modular Elliptic Curves: Book by John Cremona, with introduction, tables and software. (Elliptic Curves and Modular Forms) http://www.maths.nott.ac.uk/personal/jec/book/chapter1.html Modular Forms Example Sheets Modular Forms Example Sheets: From a course on modular forms. (Elliptic Curves and Modular Forms) http://www.math.berkeley.edu/~reb/modularforms/ Elliptic Curves Elliptic Curves: Links to research papers maintained by Stéfane Fermigier. (Elliptic Curves and Modular Forms) http://www.fermigier.com/fermigier/elliptic.html.en Elliptic Divisibility Sequences Elliptic Divisibility Sequences: Articles and links, compiled by Graham Everest. (Elliptic Curves and Modular Forms) http://www.mth.uea.ac.uk/~h090/EDS.html Torsion Points on Elliptic Curves Torsion Points on Elliptic Curves: Elementary introduction and brief explanation of some well-known results. (Elliptic Curves and Modular Forms) http://mat.uab.es/~xarles/elliptic.html A Proof of the Full Shimura-Taniyama-Weil Conjecture 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. (Elliptic Curves and Modular Forms) http://www.ams.org/notices/199911/comm-darmon.pdf Elliptic Curves II Elliptic Curves II: Lecture notes by Johan P. Hansen. (Elliptic Curves and Modular Forms) http://home.imf.au.dk/matjph/Ell-E99.html An Elementary Introduction to Elliptic Curves An Elementary Introduction to Elliptic Curves: By Len Charlap, David Robbins and Raymond Coley. Downloadable text in PostScript (.ps) format. (Elliptic Curves and Modular Forms) http://www.idaccr.org/reports/reports.html Modular Curves X_0(N) 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 and Modular Forms) http://www.maths.univ-rennes1.fr/~edix/cours/trieste.html Elliptic Curves and Formal Groups Elliptic Curves and Formal Groups: Lecture notes from a seminar J. Lubin, J.-P. Serre and J. Tate. (Elliptic Curves and Modular Forms) http://www.ma.utexas.edu/users/voloch/lst.html Rational Points on Elliptic Curves Rational Points on Elliptic Curves: A course by Jerrold Tunnell. An introduction to rational points on elliptic curves through examples. (Elliptic Curves and Modular Forms) http://www.math.rutgers.edu/~tunnell/math574.html Mathematical Things 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. (Elliptic Curves and Modular Forms) http://tom.womack.net/maths/maths.htm Richard Taylor Richard Taylor: Publications including the joint paper with Andrew Wiles which completed the proof of Fermat's Last Theorem. (Elliptic Curves and Modular Forms) http://www.math.harvard.edu/~rtaylor/ Kolyvagin Seminar 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. (Elliptic Curves and Modular Forms) http://www-math.mit.edu/~osserman/seminar/ Elliptic Curves and Their Applications to Cryptography Elliptic Curves and Their Applications to Cryptography: Web text by Andreas Enge. (Elliptic Curves and Modular Forms) http://www.lix.polytechnique.fr/Labo/Andreas.Enge/buch/buch/buch.html Bibliography for Automorphic and Modular Forms, L-Functions, Representations, and Number Theory Bibliography for Automorphic and Modular Forms, L-Functions, Representations, and Number Theory: Compiled by Paul Garrett, 1996. (Elliptic Curves and Modular Forms) http://www.math.umn.edu/~garrett/m/b/bib.html Counting Points on Elliptic Curves 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. (Elliptic Curves and Modular Forms) http://www.math.jussieu.fr/~fouquet/elliptic.html Matt Baker's Papers Matt Baker's Papers: Mainly on elliptic curves. (Elliptic Curves and Modular Forms) http://www.math.berkeley.edu/~baker/papers.html History of Elliptic Curve Rank Records History of Elliptic Curve Rank Records: A table up to rank 24 compiled by Andrej Dujella. (Elliptic Curves and Modular Forms) http://www.math.hr/~duje/tors/rankhist.html Elliptic Curves and Right Triangles Elliptic Curves and Right Triangles: Slides (GIF) of lectures by Karl Rubin at Stanford University. (Elliptic Curves and Modular Forms) http://math.stanford.EDU/~rubin/lectures/sumo/ ECDL Project ECDL Project: Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers. (Elliptic Curves and Modular Forms) http://pauillac.inria.fr/~harley/ecdl/ The Birch and Swinnerton-Dyer Conjecture 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]. (Elliptic Curves and Modular Forms) http://www.claymath.org/millennium/Birch_and_Swinnerton-Dyer_Conjecture/ On 5 and 7 Descents for Elliptic Curves On 5 and 7 Descents for Elliptic Curves: Tom Fisher's Ph.D. thesis (Cambridge, 2000) in DVI and PS format. (Elliptic Curves and Modular Forms) http://www.dpmms.cam.ac.uk/~taf1000/thesis.html Modular Forms Course Modular Forms Course: Notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators. (Elliptic Curves and Modular Forms) http://modular.fas.harvard.edu/Tables/Notes/ Papers by Richard Borcherds Papers by Richard Borcherds: Including proof of the Moonshine Conjecture (TeX,DVI,PDF). (Elliptic Curves and Modular Forms) http://www.math.berkeley.edu/~reb/papers/ Prime Values of Elliptic Divisibility Sequences Prime Values of Elliptic Divisibility Sequences: By Graham Everest. (Elliptic Curves and Modular Forms) http://www.mth.uea.ac.uk/~h090/primeEDS.html Elliptical Curve Cryptography Elliptical Curve Cryptography: Explains the difference between an elliptical curve and an ellipse. Discusses fields, applications, choosing a fixed point, and related topics. (Elliptic Curves and Modular Forms) http://www.cryptoman.com/elliptic.htm Iwasawa Theory of Elliptic Curves Iwasawa Theory of Elliptic Curves: Lecture notes and surveys by Ralph Greenberg, University of Washington (PS). (Elliptic Curves and Modular Forms) http://www.math.washington.edu/~greenber/research.html Monstrous Moonshine Monstrous Moonshine: the surprising and mysterious connections between the monster (and also other finite sporadic simple groups) and modular functions. (Elliptic Curves and Modular Forms) http://cicma.concordia.ca/faculty/cummins/moonshine.html Modular Forms and Hecke Operators Modular Forms and Hecke Operators: Notes by William A. Stein of a course by Ken Ribet. (Elliptic Curves and Modular Forms) http://modular.fas.harvard.edu/MF.html Modularity of Elliptic Curves and Beyond Modularity of Elliptic Curves and Beyond: Workshop, MSRI Berkeley, 6-10 December 1999. (Elliptic Curves and Modular Forms) http://www.msri.org/activities/events/9900/hottopics/