Inventiones mathematicae

, Volume 102, Issue 1, pp 543–618 | Cite as

Nonvanishing theorems for L-functions of modular forms and their derivatives

  • Daniel Bump
  • Solomon Friedberg
  • Jeffrey Hoffstein


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Atkin, O., Li, W.: Twists of newforms and pseudoeigenvalues ofW-operators. Invent. Math.48, 221–243 (1978)Google Scholar
  2. 2.
    Bump, D.: The Rankin-Selberg method: a survey. To appear in the proceedings of the Selberg Symposium, Oslo (1987)Google Scholar
  3. 3.
    Bump, D., Friedberg, S., Hoffstein, J.: Eisenstein series on the metaplectic group and nonvanishing theorems for automorphicL-functions and their derivatives. Ann. Math.131, 53–127 (1990)Google Scholar
  4. 4.
    Bump, D., Friedberg, S., Hoffstein, J.: A nonvanishing theorem for derivatives of automorphicL-functions with applications to elliptic curves. Bull. Am. Math. Soc. (to appear) (1989)Google Scholar
  5. 5.
    Eichler, M., Zagier, D.: The theory of Jacobi forms. Boston: Birkhäuser 1985Google Scholar
  6. 6.
    Goldfeld, D., Hoffstein, J.: Eisenstein series of 1/2-integral weight and the mean value of real DirichletL-series. Invent. Math.80, 185–208 (1985)Google Scholar
  7. 7.
    Gross, D., Zagier, D.: Heegner points and derivatives ofL-series. Invent. Math.84, 225–320 (1986)Google Scholar
  8. 8.
    Gradshteyn, I., Ryzhik, I.: Table of integrals, series and products. New York: Academic Press 1980Google Scholar
  9. 9.
    Jacquet, H.: Fonctions de Whittaker associcés aux groupes de Chevalley. Bull. Soc. Math. France95, 243–309 (1967)Google Scholar
  10. 10.
    Jacquet, H.: On the nonvanishing of someL-functions. Proc. Ind. Acad. Sci.97, 117–155 (1987)Google Scholar
  11. 11.
    Jacquet, H., Piatetski-Shapiro, I., Shalika, J.: Automorphic forms onGL(3), I, II. Ann. Math.109, 169–258 (1979)Google Scholar
  12. 12.
    Kohnen, W.: Newforms of half-integral weight. J. Reine Angew. Math.333, 32–72 (1982)Google Scholar
  13. 13.
    Kolyvagin, V.: On groups of Mordell-Weil and Shafarevich-Tate and Weil elliptic curves. Preprint, in Russian (1988)Google Scholar
  14. 14.
    Maass, H.: Siegel's Modular Forms and Dirichlet Series. Berlin-Heidelberg. New York: (Lecture Notes in Mathematics, (216). Springer 1971Google Scholar
  15. 15.
    Murty, M.R., Murty, V.K.: Mean values of derivatives of modularL-series. Preprint 1989Google Scholar
  16. 16.
    Novodvorsky, M.: AutomorphicL-functions for the symplectic groupGSp 4. In: Automorphic Forms, Representations andL-functions. AMS Proc. Symp. Pure Math.,33, 2, 87–95 (1979)Google Scholar
  17. 17.
    Ogg, A.: On a convolution ofL-series. Invent. Math.7, 297–312 (1969)Google Scholar
  18. 18.
    Shimura, G.: Introduction to the arithmetic theory of automorphic forms. Iwanami Shoten and Princeton University Press, 1971Google Scholar
  19. 19.
    Waldspurger, J.-L.: Correspondences de Shimura. In: Proceedings of the International Congress of Mathematicians, Warzawa (1983)Google Scholar
  20. 20.
    Waldspurger, J.-L.: Correspondences de Shimura et Quaternions. Preprint 1984Google Scholar
  21. 21.
    Whittaker, E., Watson, G.: A course of Modern Analysis, fourth edition. Cambridge, 1927Google Scholar
  22. 22.
    Ziegler, C.: Jacobi forms of higher degree. Abh. Math. Sem. Univ. Hamburg59, 191–224 (1989)Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Daniel Bump
    • 1
  • Solomon Friedberg
    • 1
  • Jeffrey Hoffstein
    • 1
  1. 1.Department of mathematicsStanford UniversityStanfordUSA

Personalised recommendations