Mathematische Annalen

, Volume 290, Issue 1, pp 183–207 | Cite as

On the Shimura correspondence forGSp(4)

  • Solomon Friedberg
  • Shek-Tung Wong


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  1. [BMS]
    Bass, H., Milnor, J., Serre, J.-P.: Solutions of the congruence subgroup problem forSL n(n≧3) andSp 2n(n≧2). Publ. Math. I.H.E.S.33, 59–137 (1967)Google Scholar
  2. [B]
    Bump, D.: The Rankin-Selberg method: a survey. In: Number theory, trace formulas and discrete groups: a symposium in honor of Atle Selberg. New York London: Academic Press 1989Google Scholar
  3. [BFH1]
    Bump, D., Friedberg, S., Hoffstein, J.: On Waldspurger's theorem. In: Proceedings of the conference on automorphic forms and analytic number theory. Montreal: Centre des recherches mathématiques pp. 25–36, 1990Google Scholar
  4. [BFH3]
    Bump, D., Friedberg, S., Hoffstein, J.:p-adic Whittaker functions on the metaplectic group. Duke Math. J. (in press)Google Scholar
  5. [BFH3]
    Bump, D., Friedberg, S., Hoffstein, J.: The Kubota symbol forSp(4,Q[i]). Nagoya Math. J.119, 173–188 (1990)Google Scholar
  6. [BFH4]
    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
  7. [BH1]
    Bump, D., Hoffstein, J.: Some Euler products associated with cubic metaplectic forms onGL(3). Duke Math. J.53, 1047–1072 (1986)Google Scholar
  8. [BH2]
    Bump, D., Hoffstein, J.: On Shimura's correspondence. Duke Math. J.55, 661–691 (1987)Google Scholar
  9. [F]
    Friedberg, S.: Theta series correspondences and modular forms for number fields. In: Modular Forms. Chichester: Horwood, 75–86, 1984Google Scholar
  10. [GPS]
    Gelbart, S., Piatetski-Shapiro, I.: On Shimura's correspondence for modular forms of half-integral weight. In: Representation theory and arithmetic. Berlin Heidelberg New York: Springer 1981Google Scholar
  11. [K]
    Kubota, T.: Ein arithmetischer Satz über eine Matrizengruppe. J. Reine Angew. Math.222, 55–57 (1966)Google Scholar
  12. [M]
    Murase, A.:L-functions attached to Jacobi forms of degreen. I. J. Reine Angew. Math.401, 122–156 (1989)Google Scholar
  13. [Ni]
    Niwa, S.: Modular forms of half integral weight and the integral of certain theta-functions. Nagoya Math. J.56, 147–161 (1974)Google Scholar
  14. [No]
    Novodvorsky, M.: AutomorphicL-functions for the symplectic groupGSp 4. In: Automorphic forms, representations, andL-functions. AMS Proc. Symp. Pure Math.33, part 2 (1979)Google Scholar
  15. [P]
    Patterson, S.: A cubic analogue of the theta series. I. J. Reine Angew. Math.296, 125–161 (1977)Google Scholar
  16. [Sa]
    Savin, G.: Local Shimura correspondence. Math. Ann.280, 185–190 (1988)Google Scholar
  17. [Sh]
    Shimura, G.: On modular forms of half-integral weight. Ann. Math.97, 440–481 (1973)Google Scholar
  18. [Shin]
    Shintani, T.: On construction of holomorphic cusp forms of half integral weight. Nagoya Math. J.58, 83–126 (1975)Google Scholar
  19. [So]
    Soudry, D.: TheL and γ factors for generic representations ofGSp(4, k)×GL(2, k) over a local nonarchimedean field. Duke Math. J.51, 355–394 (1984)Google Scholar
  20. [St1]
    Stark, H.: On modular forms fromL-functions in number theory. Handwritten notes 1982Google Scholar
  21. [St2]
    Stark, H.: On the transformation formula for the symplectic theta function and applications. J. Fac. Sci. Univ. Tokyo, Sect. I A29, 1–12 (1982)Google Scholar
  22. [W]
    Weil, A.: Sur certains groups d'opérateurs unitaires. Acta Math.111, 143–211 (1964)Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Solomon Friedberg
    • 1
  • Shek-Tung Wong
    • 2
  1. 1.Department of MathematicsUniversity of California, Santa CruzSanta CruzUSA
  2. 2.Mathematisches Institut, SFB 170Universität GöttingenGöttingenGermany

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