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Elliptic Curves and Modular Forms

Science > Math > Number Theory > Elliptic Curves and Modular Forms

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	http://www.loria.fr/~zimmerma/records/ecmnet.html - http://www.loria.fr/~zimmerma/records/ecmnet.html The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers.
	The Birch and Swinnerton-Dyer Conjecture - http://www.claymath.org/millennium/Birch_and_Swinnerton-Dyer_Conjecture/ A Clay Mathematics Institute Prize problem, with description by Andrew Wiles [PDF] and lecture by Fernando Rodriguez-Villegas [.ram].
	An Elementary Introduction to Elliptic Curves - http://www.idaccr.org/reports/reports.html By Len Charlap, David Robbins and Raymond Coley. Downloadable text in PostScript (.ps) format.
	Joseph Silverman - 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.
	Course Notes - 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.

	Bibliography for Automorphic and Modular Forms, L-Functions, Representations, and Number Theory - http://www.math.umn.edu/~garrett/m/b/bib.html Compiled by Paul Garrett, 1996.
	Elliptic Curves Handout - http://www.warwick.ac.uk/~masda/MA426/ Syllabus and detailed reading list by Miles Reid, University of Warwick.
	Richard Taylor - http://www.math.harvard.edu/~rtaylor/ Publications including the joint paper with Andrew Wiles which completed the proof of Fermat's Last Theorem.
	Elliptical Curve Cryptography - 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.
	History of Elliptic Curve Rank Records - http://www.math.hr/~duje/tors/rankhist.html A table up to rank 24 compiled by Andrej Dujella.

	Elliptic Curves and Right Triangles - http://math.stanford.edu/~rubin/lectures/sumo/ Slides (GIF) of lectures by Karl Rubin at Stanford University.
	14H52: Elliptic Curves - http://www.math.niu.edu/~rusin/known-math/index/14H52.html From the Known Math series.
	Elliptic Curves and Elliptic Functions - http://cgd.best.vwh.net/home/flt/flt03.htm Introductory notes by Charles Daney.
	Arithmetic of Cuves - http://math.scu.edu/~eschaefe/nt.html Papers and surveys by Ed Schaefer.
	On 5 and 7 Descents for Elliptic Curves - http://www.dpmms.cam.ac.uk/~taf1000/thesis.html Tom Fisher's Ph.D. thesis (Cambridge, 2000) in DVI and PS format.

	Kolyvagin Seminar - 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.
	Iwasawa Theory of Elliptic Curves - http://www.math.washington.edu/~greenber/research.html Lecture notes and surveys by Ralph Greenberg, University of Washington (PS).
	Elliptic Curves with H. A. Verrill - http://www.math.lsu.edu/~verrill/teaching/math7280/index.html Lecture notes and resources by Helena Verrill, Louisiana State University, 2004.
	Modular Forms Course - http://modular.fas.harvard.edu/Tables/Notes/ Notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators.
	Elliptic Functions and Elliptic Curves - http://www.math.jussieu.fr/~nekovar/co/ln/el/ Lecture notes by Jan Neková (PS/PDF).

	Prime Values of Elliptic Divisibility Sequences - http://www.mth.uea.ac.uk/~h090/primeEDS.html By Graham Everest.
	Rational Points on Elliptic Curves - http://www.math.rutgers.edu/~tunnell/math574.html A course by Jerrold Tunnell. An introduction to rational points on elliptic curves through examples.
	Mathematical Things - 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.
	Papers by Richard Borcherds - http://math.berkeley.edu/~reb/papers/ Including proof of the Moonshine Conjecture (TeX,DVI,PDF).
	Modular Forms and Hecke Operators - http://modular.fas.harvard.edu/MF.html Notes by William A. Stein of a course by Ken Ribet.

	Counting Points on Elliptic Curves - 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.
	Elliptic Curves II - http://home.imf.au.dk/matjph/Ell-E99.html Lecture notes by Johan P. Hansen.
	Torsion Points on Elliptic Curves - http://mat.uab.cat/~xarles/elliptic.html Elementary introduction and brief explanation of some well-known results.
	A Proof of the Full Shimura-Taniyama-Weil Conjecture - 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.
	Elliptic Divisibility Sequences - http://www.mth.uea.ac.uk/~h090/EDS.html Articles and links, compiled by Graham Everest.

	Recent Progress in the Theory of Elliptic Curves - 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.
	ECDL Project - http://pauillac.inria.fr/~harley/ecdl/ Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers.
	Elliptic Curves and Formal Groups - http://www.ma.utexas.edu/users/voloch/lst.html Lecture notes from a seminar J. Lubin, J.-P. Serre and J. Tate.
	Explicit Approaches to Modular Abelian Varieties - http://modular.fas.harvard.edu/papers/explicit/ William Stein, Ph.D. thesis, Berkeley, 2000.

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