Download [proceedings] in pdf format of the Clay workshop at the Newton institute, February 2004, edited by Conrey, Farmer, Mezzadri, and Snaith.
Contents
Introduction 1 J. B. Conrey, D. W. Farmer, F. Mezzadri, and N. C. Snaith
Families Elliptic curves, rank in families and random matrices 7 E. Kowalski
Modeling families of L-functions 53 D. W. Farmer
Analytic number theory and ranks of elliptic curves 71 M. P. Young
The derivative of SO(2N +1) characteristic polynomials and rank 3 elliptic curves 93
N. C. Snaith Function Żelds and random matrices 109
D. Ulmer Some applications of symmetric functions theory in random matrix theory 143
A. Gamburd Ranks of quadratic twists
The distribution of ranks in families of quadratic twists of elliptic curves 171 A. Silverberg
Twists of elliptic curves of rank at least four 177 K. Rubin and A. Silverberg
The powers of logarithm for quadratic twists 189 C. Delaunay and M. Watkins
Note on the frequency of vanishing of L-functions of elliptic curves in a family of quadratic twists 195 C. Delaunay
Discretisation for odd quadratic twists 201 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 215 J. B. Conrey, A. Pokharel, M. O. Rubinstein and M. Watkins
Fudge Factors in the Birch and Swinnerton-Dyer Conjecture 233 K. Rubin
Number fields and higher twists Rank distribution in a family of cubic twists 237 M. Watkins
Vanishing of L-functions of elliptic curves over number Fields 247 C. David, J. Fearnley and H. Kisilevsky
Shimura correspondence, and twists Computing central values of L-functions 260 F. Rodriguez-Villegas
Computation of central value of quadratic twists of modular Lˇfunctions 273 Z. Mao, F. Rodriguez-Villegas and G. Tornaria
Examples of Shimura correspondence for level p2 and real quadratic twists 289 A. Pacetti and G. Tornaria
Central values of quadratic twists for a modular form of weight 4 315 H. Rosson and G. Tornaria
Global structure: Sha and descent Heuristics on class groups and on Tate-Shafarevich groups 323 C. Delaunay
A Note on the 2-Part of X for the Congruent Number Curves 341 D.R. Heath-Brown
2-Descent Through the Ages 345 P. Swinnerton-Dyer
Back to the
main index
for Random Matrix Theory and central vanishing of L-functions.