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Ranks of elliptic curves and random matrix theory

By: Contributor(s): Material type: TextTextLanguage: English Series: London mathematical society lecture note series ; 341Publication details: Cambridge Cambridge University Press 2007Description: vi, 361pISBN:
  • 9780521699648 (PB)
Subject(s):
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
Summary: This comprehensive volume introduces elliptic curves and the fundamentals of modeling by a family of random matrices.
Item type: BOOKS
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IMSc Library 512.742(082)“2007”CON (Browse shelf(Opens below)) Available 62563

Includes index.

Includes bibliography (p. 356) and references.

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

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

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