Home > Science > Math > Number Theory > Elliptic Curves and Modular Forms
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.
http://www.ams.org/notices/199911/comm-darmon.pdf
Article by Henri Darmon on the completion of the proof by Wiles, Breuil, Conrad, Diamond and Taylor.
http://homepages.warwick.ac.uk/staff/J.E.Cremona/book/
Book by John Cremona, with introduction, tables and software.
http://math.scu.edu/~eschaefe/nt.html
Papers and surveys by Ed Schaefer.
http://www.math.umn.edu/~garrett/m/b/bib.html
Compiled by Paul Garrett, 1996.
http://www.math.jussieu.fr/~fouquet/elliptic.html
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.jmilne.org/math/CourseNotes/
Full notes as .dvi, .pdf, and .ps files for all the advanced courses J. S. Milne taught between 1986 and 1999.
http://pauillac.inria.fr/~harley/ecdl/
Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers.
http://www.loria.fr/~zimmerma/records/ecmnet.html
The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers.
http://www.scienceandreason.net/flt/flt03.htm
Introductory notes by Charles Daney.
http://www.ma.utexas.edu/users/voloch/lst.html
Lecture notes from a seminar J. Lubin, J.-P. Serre and J. Tate.
http://www.warwick.ac.uk/~masda/MA426/
Syllabus and detailed reading list by Miles Reid, University of Warwick.
http://home.imf.au.dk/matjph/Ell-E99.html
Lecture notes by Johan P. Hansen.
http://www.math.jussieu.fr/~nekovar/co/ln/el/
Lecture notes by Jan Nekovář (PS/PDF).
http://www.cryptoman.com/elliptic.htm
Explains the difference between an elliptical curve and an ellipse. Discusses fields, applications, choosing a fixed point, and related topics.
http://wstein.org/papers/thesis/
William Stein, Ph.D. thesis, Berkeley, 2000.
http://www.math.hr/~duje/tors/rankhist.html
A table up to rank 24 compiled by Andrej Dujella.
http://www.math.washington.edu/~greenber/research.html
Lecture notes and surveys by Ralph Greenberg, University of Washington (PS).
http://www.math.brown.edu/~jhs/
Includes errata for his books Rational Points on Elliptic Curves and Advanced Topics in the Arithmetic of Elliptic Curves.
http://math.berkeley.edu/~osserman/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://tom.womack.net/maths/maths.htm
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://math.berkeley.edu/~reb/courses/modularforms/index.html
From a course on modular forms.
http://www.dpmms.cam.ac.uk/~taf1000/thesis.html
Tom Fisher's Ph.D. thesis (Cambridge, 2000) in DVI and PS format.
http://math.berkeley.edu/~reb/papers/
Including proof of the Moonshine Conjecture (TeX,DVI,PDF).
http://www.math.rutgers.edu/~tunnell/math574.html
A course by Jerrold Tunnell. An introduction to rational points on elliptic curves through examples.
http://www.cms.math.ca/CMS/Events/winter98/w98-abs/node2.html
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.math.ias.edu/~rtaylor
Publications including the joint paper with Andrew Wiles which completed the proof of Fermat's Last Theorem.
http://mat.uab.cat/~xarles/elliptic.html
Elementary introduction and brief explanation of some well-known results.
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