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Home / Science / Math / Number Theory / Elliptic Curves and Modular Forms
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Web Sites
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- 14H52: Elliptic Curves - From the Known Math series.
www.math.niu.edu/~rusin/known-math/index/14H52.html
- 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.
www.ams.org/notices/199911/comm-darmon.pdf
- Algorithms for Modular Elliptic Curves - Book by John Cremona, with introduction, tables and software.
www.maths.nott.ac.uk/personal/jec/book/chapter1.html
- An Elementary Introduction to Elliptic Curves - By Len Charlap, David Robbins and Raymond Coley. Downloadable text in PostScript (.ps) format.
www.idaccr.org/reports/reports.html
- Andreas Enge - Krypto - Includes the text of the author's introductory book to elliptic curves and their applications in cryptography.
www.math.uni-augsburg.de/~enge/Krypto.html
- Arithmetic of Cuves - Papers and surveys by Ed Schaefer.
math.scu.edu/~eschaefe/nt.html
- Bibliography for Automorphic and Modular Forms, L-Functions, Representations, and Number Theory - Compiled by Paul Garrett, 1996.
www.math.umn.edu/~garrett/m/b/bib.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 due to Takakazu Satoh.
www.lix.polytechnique.fr/Labo/Mireille.Fouquet/elliptic.html
- Course Notes - Full notes as .dvi, .pdf, and .ps files for all the advanced courses J. S. Milne taught between 1986 and 1999.
www.jmilne.org/math/CourseNotes
- David Pollack - The author's thesis "Explicit Hecke Actions on Modular Forms, Harvard, 1998" is available here in DVI form.
www.math.ohio-state.edu/~pollack
- Douglas Ulmer's Publications and Preprints - Mainly on elliptic curves and modular forms.
swc.math.arizona.edu/~ulmer/research/papers.html
- ECDL Project - Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers.
pauillac.inria.fr/~harley/ecdl
- ECMNET - The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers.
www.loria.fr/~zimmerma/records/ecmnet.html
- Elliptic Curves - Links to research papers maintained by Stéfane Fermigier.
www.fermigier.com/fermigier/elliptic.html.en
- Elliptic Curves and Cryptology - Marc Joye's list of elliptic curve resources includes people, books, and links. Many preprints are available from the site.
www.geocities.com/marcjoye/biblio_ell.html
- Elliptic Curves and Elliptic Functions - Introductory notes by Charles Daney.
cgd.best.vwh.net/home/flt/flt03.htm
- Elliptic Curves and Formal Groups - Lecture notes from a seminar J. Lubin, J.-P. Serre and J. Tate.
www.ma.utexas.edu/users/voloch/lst.html
- Elliptic Curves and Right Triangles - Slides (GIF) of lectures by Karl Rubin at Stanford University.
math.stanford.EDU/~rubin/lectures/sumo
- Elliptic Curves Handout - Syllabus and detailed reading list by Miles Reid, University of Warwick.
www.maths.warwick.ac.uk/~miles/MA426
- Elliptic Curves II - Lecture notes by Johan P. Hansen.
home.imf.au.dk/matjph/Ell-E99.html
- Elliptic Divisibility Sequences - Articles and links, compiled by Graham Everest.
www.mth.uea.ac.uk/~h090/EDS.html
- Explicit Approaches to Modular Abelian Varieties - William Stein, Ph.D. thesis, Berkeley, 2000.
modular.fas.harvard.edu/papers/explicit
- Iwasawa Theory of Elliptic Curves - Lecture notes and surveys by Ralph Greenberg, University of Washington (PS).
www.math.washington.edu/~greenber/research.html
- Joseph Silverman - Includes errata for his books Rational Points on Elliptic Curves and Advanced Topics in the Arithmetic of Elliptic Curves.
www.math.brown.edu/~jhs
- 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.
www-math.mit.edu/~osserman/seminar
- 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.
tom.womack.net/maths/maths.htm
- Matt Baker's Papers - Mainly on elliptic curves.
www.math.berkeley.edu/~baker/papers.html
- 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.
www.maths.univ-rennes1.fr/~edix/cours/trieste.html
- Modular Forms and Hecke Operators - Notes by William A. Stein of a course by Ken Ribet.
modular.fas.harvard.edu/MF.html
- Modular Forms Course - Notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators.
modular.fas.harvard.edu/Tables/Notes
- Modular Forms Example Sheets - From a course on modular forms.
www.math.berkeley.edu/~reb/modularforms
- Modularity of Elliptic Curves and Beyond - Workshop, MSRI Berkeley, 6-10 December 1999.
www.msri.org/activities/events/9900/hottopics
- Monstrous Moonshine - the surprising and mysterious connections between the monster (and also other finite sporadic simple groups) and modular functions.
cicma.concordia.ca/faculty/cummins/moonshine.html
- Moonshine Bibliography - Books and papers relating to the Conway-Norton-Thompson Moonshine conjecture, proved by Richard Borcherds.
cicma.concordia.ca/faculty/cummins/moonshine.refs.html
- On 5 and 7 Descents for Elliptic Curves - Tom Fisher's Ph.D. thesis (Cambridge, 2000) in DVI and PS format.
www.dpmms.cam.ac.uk/~taf1000/thesis.html
- Papers by Richard Borcherds - Including proof of the Moonshine Conjecture (TeX,DVI,PDF).
www.math.berkeley.edu/~reb/papers
- Prime Values of Elliptic Divisibility Sequences - By Graham Everest.
www.mth.uea.ac.uk/~h090/primeEDS.html
- Publications of François Morain - Thesis and papers on elliptic curves, especially primality proofs and point counting.
ultralix.polytechnique.fr/~morain/Articles/articles.english.html
- Rational Points on Elliptic Curves - A course by Jerrold Tunnell. An introduction to rational points on elliptic curves through examples.
www.math.rutgers.edu/~tunnell/math574.html
- 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.
www.cms.math.ca/CMS/Events/winter98/w98-abs/node2.html
- Richard Taylor - Publications including the joint paper with Andrew Wiles which completed the proof of Fermat's Last Theorem.
www.math.harvard.edu/~rtaylor
- Satoh-FGH algorithm - Gonzalez and Harley explain Professor Satoh's elliptic curve point counting algorithm.
argote.ch/Research.html
- The Birch and Swinnerton-Dyer Conjecture - A Clay Mathematics Institute Prize problem, with PDF description by Andrew Wiles. The conjecture addresses the problem of enumerating rational points, such as on elliptic curves.
www.claymath.org/prize_problems/birchsd.htm
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