Ranks of Elliptic Curves and Random Matrix Theory /

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

Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Conrey, J. B., Farmer, D. W., Mezzadri, F., Snaith, N. C.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 2007.
Colección:London Mathematical Society lecture note series ; no. 341.
Temas:
Curves, Elliptic > Congresses.
Random matrices > Congresses.
Courbes elliptiques > Congrès.
Matrices aléatoires > Congrès.
MATHEMATICS > Geometry > Algebraic.
Curves, Elliptic.
Random matrices.
Conference papers and proceedings.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

Ejemplares similares