Advertisement

Conjectures on elliptic curves over quadratic fields

  • Dorian Goldfeld
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 751)

Keywords

Modular Form Elliptic Curve Elliptic Curf Eisenstein Series Cusp Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. M. B. Barban, "Linnik's ‘large sieve’ and a limit theorem for the class number of ideals of an imaginary quadratic field," Izk. Nauk SSSR, Ser. Mat. [1962], 573–78.Google Scholar
  2. Birch and Swinnerton-Dyer, "Elliptic curves and modular functions," Modular functions of one variable, Springer Lecture Notes 476 [1975], 2–32.MathSciNetzbMATHGoogle Scholar
  3. J. Coates and A. Wiles, "On the conjecture of Birch and Swinnerton-Dyer," Inventiones Math. 39, [1977], 223–251.MathSciNetCrossRefzbMATHGoogle Scholar
  4. D. Goldfeld and C. Viola, "Mean values of L-functions associated to elliptic, Fermat and other curves at the center of the critical strip," to appear J. Number Theory [1979].Google Scholar
  5. E. Hecke, "Neue Herleitung der Klassenzahlrelationen von Hurwitz und Kronecker," Nachrichten der K. Gesellschaft der Wissenschaften zu Göttingen, Math.-Phys. Klasse [1926], 244–249.Google Scholar
  6. A. F. Lavrik, "Functional equations of Dirichlet functions," Soviet Math. Dokl. 7 [1966], 1471–1473.MathSciNetzbMATHGoogle Scholar
  7. R. A. Rankin, "Contributions to the theory of Ramanujan's function τ(n) and similar arithmetic functions," Proc. Cambridge Philos. Soc. 35 [1939], 357–375.MathSciNetCrossRefzbMATHGoogle Scholar
  8. G. Shimura, Arithmetic theory of automorphic functions, Princeton Univ. Press [1971], 183–184.Google Scholar
  9. T. Shintani, "On zeta functions associated with prehomogeneous vector spaces," Seminar on Modern Methods in Number Theory, Inst. Statist. Math. Tokyo [1971], paper no. 40.Google Scholar
  10. B. V. Stepanov, "On the mean value of the kth power of the number of classes for an imaginary quadratic field," Dokl. Akad. Nauk SSSR 124 [1959], 984–986.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Dorian Goldfeld
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridge

Personalised recommendations