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Elliptic Curves and Modular Forms


Elliptic Curves and Modular Forms
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14H52: Elliptic Curves open in new window
From the Known Math series.
(http://www.math.niu.edu/~rusin/known-math/index/14H52.html)

A Proof of the Full Shimura-Taniyama-Weil Conjecture open in new window
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-darmon.pdf)

Algorithms for Modular Elliptic Curves open in new window
Book by John Cremona, with introduction, tables and software.
(http://www.maths.nott.ac.uk/personal/jec/book/chapter1.html)

An Elementary Introduction to Elliptic Curves open in new window
By Len Charlap, David Robbins and Raymond Coley. Downloadable text in PostScript (.ps) format.
(http://www.idaccr.org/reports/reports.html)

Arithmetic of Cuves open in new window
Papers and surveys by Ed Schaefer.
(http://math.scu.edu/~eschaefe/nt.html)

Bibliography for Automorphic and Modular Forms, L-Functions, Representations, and Number Theory open in new window
Compiled by Paul Garrett, 1996.
(http://www.math.umn.edu/~garrett/m/b/bib.html)

Counting Points on Elliptic Curves open in new window
Robert Harley, Pierrick Gaudry, François Morain and Mireille Fouquet have established new records for point counting in characteristic 2, using a new algorithm due to Takakazu Satoh.
(http://www.lix.polytechnique.fr/Labo/Mireille.Fouquet/ellipt)

Course Notes open in new window
Full notes as .dvi, .pdf, and .ps files for all the advanced courses J. S. Milne taught between 1986 and 1999.
(http://www.jmilne.org/math/CourseNotes/)

David Pollack open in new window
The author's thesis "Explicit Hecke Actions on Modular Forms, Harvard, 1998" is available here in DVI form.
(http://www.math.ohio-state.edu/~pollack/)

Douglas Ulmer's Publications and Preprints open in new window
Mainly on elliptic curves and modular forms.
(http://swc.math.arizona.edu/~ulmer/research/papers.html)

ECDL Project open in new window
Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers.
(http://pauillac.inria.fr/~harley/ecdl/)

ECMNET open in new window
The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers.
(http://www.loria.fr/~zimmerma/records/ecmnet.html)

Elliptic Curves open in new window
Links to research papers maintained by Stéfane Fermigier.
(http://www.fermigier.com/fermigier/elliptic.html.en)

Elliptic Curves and Cryptology open in new window
Marc Joye's list of elliptic curve resources includes people, books, and links. Many preprints are available from the site.
(http://www.geocities.com/marcjoye/biblio_ell.html)

Elliptic Curves and Elliptic Functions open in new window
Introductory notes by Charles Daney.
(http://cgd.best.vwh.net/home/flt/flt03.htm)

Elliptic Curves and Formal Groups open in new window
Lecture notes from a seminar J. Lubin, J.-P. Serre and J. Tate.
(http://www.ma.utexas.edu/users/voloch/lst.html)

Elliptic Curves and Right Triangles open in new window
Slides (GIF) of lectures by Karl Rubin at Stanford University.
(http://math.stanford.EDU/~rubin/lectures/sumo/)

Elliptic Curves Handout open in new window
Syllabus and detailed reading list by Miles Reid, University of Warwick.
(http://www.maths.warwick.ac.uk/~miles/MA426/)

Elliptic Curves II open in new window
Lecture notes by Johan P. Hansen.
(http://home.imf.au.dk/matjph/Ell-E99.html)

Elliptic Divisibility Sequences open in new window
Articles and links, compiled by Graham Everest.
(http://www.mth.uea.ac.uk/~h090/EDS.html)

Explicit Approaches to Modular Abelian Varieties open in new window
William Stein, Ph.D. thesis, Berkeley, 2000.
(http://modular.fas.harvard.edu/papers/explicit/)

Iwasawa Theory of Elliptic Curves open in new window
Lecture notes and surveys by Ralph Greenberg, University of Washington (PS).
(http://www.math.washington.edu/~greenber/research.html)

Joseph Silverman open in new window
Includes errata for his books Rational Points on Elliptic Curves and Advanced Topics in the Arithmetic of Elliptic Curves.
(http://www.math.brown.edu/~jhs/)

Kolyvagin Seminar open in new window
A semester-long seminar studying Kolyvagin's application of Euler systems to elliptic curves. Includes extensive lecture notes in PostScript or DVI format.
(http://www-math.mit.edu/~osserman/seminar/)

Mathematical Things open in new window
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)

Matt Baker's Papers open in new window
Mainly on elliptic curves.
(http://www.math.berkeley.edu/~baker/papers.html)

Modular Curves X_0(N) open in new window
A series of lectures by Bas Edixhoven at the ICTP Summer school on rational torsion of elliptic curves over number fields.
(http://www.maths.univ-rennes1.fr/~edix/cours/trieste.html)

Modular Forms and Hecke Operators open in new window
Notes by William A. Stein of a course by Ken Ribet.
(http://modular.fas.harvard.edu/MF.html)

Modular Forms Course open in new window
Notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators.
(http://modular.fas.harvard.edu/Tables/Notes/)

Modular Forms Example Sheets open in new window
From a course on modular forms.
(http://www.math.berkeley.edu/~reb/modularforms/)

Modularity of Elliptic Curves and Beyond open in new window
Workshop, MSRI Berkeley, 6-10 December 1999.
(http://www.msri.org/activities/events/9900/hottopics/)

Monstrous Moonshine open in new window
the surprising and mysterious connections between the monster (and also other finite sporadic simple groups) and modular functions.
(http://cicma.concordia.ca/faculty/cummins/moonshine.html)

Moonshine Bibliography open in new window
Books and papers relating to the Conway-Norton-Thompson Moonshine conjecture, proved by Richard Borcherds.
(http://cicma.concordia.ca/faculty/cummins/moonshine.refs.htm)

On 5 and 7 Descents for Elliptic Curves open in new window
Tom Fisher's Ph.D. thesis (Cambridge, 2000) in DVI and PS format.
(http://www.dpmms.cam.ac.uk/~taf1000/thesis.html)

Papers by Richard Borcherds open in new window
Including proof of the Moonshine Conjecture (TeX,DVI,PDF).
(http://www.math.berkeley.edu/~reb/papers/)

Prime Values of Elliptic Divisibility Sequences open in new window
By Graham Everest.
(http://www.mth.uea.ac.uk/~h090/primeEDS.html)

Publications of François Morain open in new window
Thesis and papers on elliptic curves, especially primality proofs and point counting.
(http://ultralix.polytechnique.fr/~morain/Articles/articles.e)

Rational Points on Elliptic Curves open in new window
A course by Jerrold Tunnell. An introduction to rational points on elliptic curves through examples.
(http://www.math.rutgers.edu/~tunnell/math574.html)

Recent Progress in the Theory of Elliptic Curves open in new window
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/w98-abs/node2.htm)

Richard Taylor open in new window
Publications including the joint paper with Andrew Wiles which completed the proof of Fermat's Last Theorem.
(http://www.math.harvard.edu/~rtaylor/)

Satoh-FGH algorithm open in new window
Gonzalez and Harley explain Professor Satoh's elliptic curve point counting algorithm.
(http://argote.ch/Research.html)

The Birch and Swinnerton-Dyer Conjecture open in new window
A Clay Mathematics Institute Prize problem, with description by Andrew Wiles [PDF] and lecture by Fernando Rodriguez-Villegas [.ram].
(http://www.claymath.org/Millennium_Prize_Problems/Birch_and_)

Torsion Points on Elliptic Curves open in new window
Elementary introduction and brief explanation of some well-known results.
(http://mat.uab.es/xarles/elliptic/elliptic.html)


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