Lukol Directory: Science: Math: Number Theory: Elliptic Curves and Modular Forms

Prime Values of Elliptic Divisibility Sequences By Graham Everest. http://www.mth.uea.ac.uk/~h090/primeEDS.ht... 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. http://www.cms.math.ca/CMS/Events/winter98... 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]. http://www.claymath.org/millennium/Birch_a... History of Elliptic Curve Rank Records A table up to rank 24 compiled by Andrej Dujella. http://www.math.hr/~duje/tors/rankhist.htm... Elliptic Curves Links to research papers maintained by Stéfane Fermigier. http://www.fermigier.com/fermigier/ellipti... 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. http://tom.womack.net/maths/maths.htm Papers by R. E. Borcherds Including proof of the Moonshine Conjecture (TeX, DVI, PDF). http://math.berkeley.edu/~reb/papers/ 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. http://math.berkeley.edu/~osserman/seminar... An Elementary Introduction to Elliptic Curves By Len Charlap, David Robbins and Raymond Coley. Downloadable text in PostScript (.ps) format. http://www.idaccr.org/reports/reports.html Elliptical Curve Cryptography Explains the difference between an elliptical curve and an ellipse. Discusses fields, applications, choosing a fixed point, and related topics. http://www.cryptoman.com/elliptic.htm Elliptic Curves and Cryptology Marc Joye's list of resources that include people, books, and links. Many preprints are available from the site. http://www.geocities.com/marcjoye/biblio_e... Elliptic Curves Handout Syllabus and detailed reading list by Miles Reid, University of Warwick. http://www.maths.warwick.ac.uk/~miles/MA42... Elliptic Curves and Formal Groups Lecture notes from a seminar J. Lubin, J.-P. Serre and J. Tate. http://www.ma.utexas.edu/users/voloch/lst.... Arithmetic of Cuves Papers and surveys by Ed Schaefer. http://math.scu.edu/~eschaefe/nt.html Modular Forms Example Sheets From a course on modular forms. http://math.berkeley.edu/~reb/modularforms... Explicit Approaches to Modular Abelian Varieties William Stein, Ph.D. thesis, Berkeley, 2000. http://modular.fas.harvard.edu/papers/expl... Bibliography for Automorphic and Modular Forms, L-Functions, Representations, and Number Theory Compiled by Paul Garrett, 1996. http://www.math.umn.edu/~garrett/m/b/bib.h... Elliptic Functions and Elliptic Curves Lecture notes by Jan Nekovář (PS/PDF). http://www.math.jussieu.fr/~nekovar/co/ln/... Elliptic Curves II Lecture notes by Johan P. Hansen. http://home.imf.au.dk/matjph/Ell-E99.html 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. http://www.math.jussieu.fr/~fouquet/ellipt... ECDL Project Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers. http://pauillac.inria.fr/~harley/ecdl/ Rational Points on Elliptic Curves A course by Jerrold Tunnell. An introduction to rational points on elliptic curves through examples. http://www.math.rutgers.edu/~tunnell/math5... 14H52: Elliptic Curves From the Known Math series. http://www.math.niu.edu/~rusin/known-math/... Abstract Algebra Course notes by J.S. Milne. Topics covered are group, fields and Galois, algebraic number, class field theories. Other areas discussed are modular functions and forms, elliptic curves, algebraic geometry, Etale Cohomology, and Abelian varieties. In HTML, PDF, PostScript and DVI formats. http://www.jmilne.org/math/CourseNotes/ Modular Forms Course Notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators. http://modular.fas.harvard.edu/Tables/Note... Iwasawa Theory of Elliptic Curves Lecture notes and surveys by Ralph Greenberg, University of Washington (PS). http://www.math.washington.edu/~greenber/r... Moonshine Bibliography Books and papers relating to the Conway-Norton-Thompson Moonshine conjecture, proved by Richard Borcherds. http://cicma.concordia.ca/faculty/cummins/... Elliptic Divisibility Sequences Articles and links, compiled by Graham Everest. http://www.mth.uea.ac.uk/~h090/EDS.html Monstrous Moonshine the surprising and mysterious connections between the monster (and also other finite sporadic simple groups) and modular functions. http://cicma.concordia.ca/faculty/cummins/... Elliptic Curves and Right Triangles Slides (GIF) of lectures by Karl Rubin at Stanford University. http://math.stanford.edu/~rubin/lectures/s... Torsion Points on Elliptic Curves Elementary introduction and brief explanation of some well-known results. http://mat.uab.cat/~xarles/elliptic.html On 5 and 7 Descents for Elliptic Curves Tom Fisher's Ph.D. thesis (Cambridge, 2000) in DVI and PS format. http://www.dpmms.cam.ac.uk/~taf1000/thesis... Richard Taylor Publications including the joint paper with Andrew Wiles which completed the proof of Fermat's Last Theorem. http://www.math.harvard.edu/~rtaylor/ ECMNET Project to factor numbers using the elliptic curve method. Client and server software. http://www.loria.fr/~zimmerma/records/ecmn... Elliptic Curves and Their Applications to Cryptography Web text by Andreas Enge. http://www.lix.polytechnique.fr/Labo/Andre... Elliptic Curves and Elliptic Functions Introductory notes by Charles Daney. http://cgd.best.vwh.net/home/flt/flt03.htm Silverman, Joseph Mathematician at Brown University, with links to publications and courses. http://www.math.brown.edu/~jhs/ Modular Forms and Hecke Operators Notes by William A. Stein of a course by Ken Ribet. http://modular.fas.harvard.edu/MF.html Algorithms for Modular Elliptic Curves Book by John Cremona, with introduction, tables and software. http://www.maths.nott.ac.uk/personal/jec/b... 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. http://www.ams.org/notices/199911/comm-dar... Elliptic Curves with H. A. Verrill Lecture notes and resources by Helena Verrill, Louisiana State University, 2004. http://www.math.lsu.edu/~verrill/teaching/... Sub Topics: Tables Software Related Topics: Science: Math: Number Theory: Diophantine Equations: Fermat's Last Theorem Science: Math: Number Theory: Factoring Science: Math: Number Theory: Prime Numbers: Primality Tests: Primality Proving

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2006