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Inventiones mathematicae

, Volume 79, Issue 1, pp 79–94 | Cite as

On the critical values of HeckeL-functions for imaginary quadratic fields

  • Ralph Greenberg
Article

Keywords

Quadratic Field Imaginary Quadratic Field 
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References

  1. 1.
    Frohlich, A., Queyrut, J.: On the functional equation of the ArtinL-function for characters of real representations. Invent. Math.14, 179–183 (1971)Google Scholar
  2. 2.
    Greenberg, R.: On the Birch and Swinnerton-Dyer conjecture. Invent. Math.72, 241–265 (1983)Google Scholar
  3. 3.
    Gross, B.: Arithmetic on elliptic curves with complex multiplication. Lecture Notes in Math., vol. 776. Berlin-Heidelberg-New York: Springer 1980Google Scholar
  4. 4.
    Gross, B., Zagier, D.: On the critical values of HeckeL-series. Soc. Math. de France, Memoire No.2, 49–54 (1980)Google Scholar
  5. 5.
    Katz, N.:p-adic interpolation of real analytic Eisenstein series. Ann. of Math.104, 459–571 (1976)Google Scholar
  6. 6.
    Lang, S.: Algebraic Number Theory. Reading, MA: Addison-Wesley 1970Google Scholar
  7. 7.
    Manin, J., Vishik, S.:p-adic Hecke series for imaginary quadratic fields. Math. Sbornik (137)95, (No. 3.) (1974)Google Scholar
  8. 8.
    Mazur, B., Swinnerton-Dyer, H.P.F.: Arithmetic of Weil Curves. Invent. Math.25, 1–61 (1974)Google Scholar
  9. 9.
    Ogg, A.: Modular Forms and Dirichlet Series. New York: Benjamin 1969Google Scholar
  10. 10.
    Rohrlich, D.: The non-vanishing of certain HeckeL-functions at the center of the critical strip. Duke Math. J.47, 223–232 (1980)Google Scholar
  11. 11.
    Rohrlich, D.: On theL-functions of canonical Hecke characters of imaginary quadratic fields. Duke Math. J.47, 547–557 (1980)Google Scholar
  12. 12.
    Rohrlich, D.: Root numbers of HeckeL-functions of CM fields. Amer. J. of Math.104, 517–543 (1982)Google Scholar
  13. 12′.
    Rohrlich, D.: OnL-functions of elliptic curves and anticyclotomic towers. Invent. Math.75, 383–408 (1984)Google Scholar
  14. 12″.
    Rohrlich, D.: OnL-functions of elliptic curves and cyclotomic towers. Invent. Math.75, 409–423 (1984)Google Scholar
  15. 13.
    Rubin, K.: Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer. Invent. Math.64, 455–470 (1981).Google Scholar
  16. 14.
    Shimura, G.: On elliptic curves with complex multiplication as factors of the Jacobian of modular function fields. Nagoya Math. J.43, 199–208 (1971)Google Scholar
  17. 15.
    Weil, A.: On a certain type of character of the idele-class group of an algebraic number field, Proc. Int'l. Symp. Tokyo-Nikko, 1–7 (1955).Google Scholar
  18. 16.
    Weil, A.: Dirichlet Series and Automorphic Forms. Lecture Notes in Math. vol. 189. Berlin-Heidelberg-New York: Springer 1971Google Scholar
  19. 17.
    Yager, R.: On two-variablep-adicL-functions. Ann. of Math.115, 411–449 (1982)Google Scholar
  20. 18.
    Yager, R.:p-adic measures in Galois groups. PreprintGoogle Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Ralph Greenberg
    • 1
  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

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