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Ranks of elliptic curves and random matrix theory

Author: J B Conrey; Isaac Newton Institute for Mathematical Sciences.; Clay Mathematics Institute.; et al
Publisher: Cambridge, UK ; New York : Cambridge University Press, 2007.
Series: London Mathematical Society lecture note series, 341.
Edition/Format:   Book : Conference publication : EnglishView all editions and formats
Database:WorldCat
Summary:

This comprehensive volume introduces elliptic curves and the fundamentals of modeling by a family of random matrices.

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Genre/Form: Conference proceedings
Congresses
Material Type: Conference publication, Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: J B Conrey; Isaac Newton Institute for Mathematical Sciences.; Clay Mathematics Institute.; et al
ISBN: 9780521699648 0521699649
OCLC Number: 81452671
Notes: "Many ... of the papers here have origins in a workshop that took place at the Isaac Newton Institute in February of 2004 entitled "Clay Mathematics Institute Special week on Ranks of Elliptic Curves and Random Matrix Theory"--Introd.
Description: vi, 361 p. : ill. ; 23 cm.
Contents: Introduction J.B. Conrey, D.W. Farmer, F. Mezzadri and N.C. Snaith --
Part I. Families: Elliptic curves, rank in families and random matrices E. Kowalski --
Modeling families of L-functions D.W. Farmer --
Analytic number theory and ranks of elliptic curves M.P. Young --
The derivative of SO(2N +1) characteristic polynomials and rank 3 elliptic curves N.C. Snaith --
Function fields and random matrices D. Ulmer --
Some applications of symmetric functions theory in random matrix theory A. Gamburd --
Part II. Ranks of Quadratic Twists --
The distribution of ranks in families of quadratic twists of elliptic curves A. Silverberg --
Twists of elliptic curves of rank at least four K. Rubin and A. Silverberg --
The powers of logarithm for quadratic twists C. Delaunay and M. Watkins --
Note on the frequency of vanishing of L-functions of elliptic curves in a family of quadratic twists C. Delaunay --
Discretisation for odd quadratic twists J.B. Conrey, M.O. Rubinstein, N.C. Snaith and M. Watkins --
Secondary terms in the number of vanishings of quadratic twists of elliptic curve L-functions J.B. Conrey, A. Pokharel, M.O. Rubinstein and M. Watkins --
Fudge factors in the Birch and Swinnerton-Dyer Conjecture K. Rubin --
Part III. Number Fields and Higher Twists --
Rank distribution in a family of cubic twists M. Watkins --
Vanishing of L-functions of elliptic curves over number fields C. David, J. Fearnley and H. Kisilevsky --
Part IV. Shimura Correspondence, and Twists --
Computing central values of L-functions F. Rodriguez-Villegas --
Computation of central value of quadratic twists of modular L-functions Z. Mao, F. Rodriguez-Villegas and G. Tornaria --
Examples of Shimura correspondence for level p2 and real quadratic twists A. Pacetti and G. Tornaria --
Central values of quadratic twists for a modular form of weight H. Rosson and G. Tornaria --
Part V. Global Structure: Sha and Descent --
Heuristics on class groups and on Tate-Shafarevich groups C. Delaunay --
A note on the 2-part of X for the congruent number curves D.R. Heath-Brown --
2-Descent tThrough the ages P. Swinnerton-Dyer.
Series Title: London Mathematical Society lecture note series, 341.
Responsibility: edited by J.B. Conrey ... [et al.].
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'Due to these expository lectures, the book may well be of help to newcomers to the field.' European Mathematical Society Newsletter

 
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