Inventiones mathematicae

, Volume 107, Issue 1, pp 61–86 | Cite as

Theta functions on then-fold metaplectic cover of SL(2)—the function field case

  • Jeffrey Hoffstein


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bump, D., Hoffstein, J.: Some conjectured relationships between theta functions and Eisenstein series on the metaplectic group. In: Chudnovsky, D.V. et al. (eds.) Proceedings of the New York Number Theory Seminar. (Lect. Notes Math., vol. 1383, pp. 1–11) Berlin Heidelberg New York: Springer 1989Google Scholar
  2. 2.
    Deligne, P.: Sommes de Gauss cubiques et revêtements de SL(2). (Lect. Notes Math., vol. 770, pp. 244–277), Berlin Heidelberg New York: Springer 1980Google Scholar
  3. 3.
    Heath-Brown, D.R., Patterson, S.J.: The distribution of Kummer sums at prime arguments. J. Reine Angew. Math.310, 111–130 (1979)Google Scholar
  4. 4.
    Hoffstein, J., Rosen, M.: Average values ofL-series in function fields. J. Reine Angew. Math. (to appear)Google Scholar
  5. 5.
    Kazhdan, D.A., Patterson, S.J.: Metaplectic forms. Publ. Math., Inst. Hautes Étud. Sci.,59, 35–142 (1984)Google Scholar
  6. 6.
    Kubota, T.: On automorphic forms and the reciprocity law in a number field. Tokyo: Kinokuniya Book Store Co. 1969Google Scholar
  7. 7.
    Patterson, S.J.: A cubic analogue of the theta series. J. Reine Angew. Math.296, 125–161 (1977)Google Scholar
  8. 8.
    Patterson, S.J.: Wittaker models of generalized theta series. In: Bertini, M.-J., Goldstein, C. (eds.) Sém. de th. des nombres. Paris, 1982–83. Boston: Birkhäuser 1984Google Scholar
  9. 9.
    Shimura, G.: On modular forms of half-integral weight. Ann. Math.97 (1973)Google Scholar
  10. 10.
    Suzuki, T.: Some results on the coefficients of the biquadratic theta series. J. Reine Angew. Math.340, 70–117 (1982)Google Scholar
  11. 11.
    Suzuki, T.: Rankin-Selberg convolutions of generalized theta series. J. Reine Angew. Math. (to appear)Google Scholar
  12. 12.
    Weil, A.: Sur certaines groupes d'operateurs unitaire. Acta Math.111, 143–211 (1964)Google Scholar
  13. 13.
    Zagier, D.: The Rankin-Selberg method for automorphic functions which are not of rapid decay. J. Fac. Sci. Univ. of Tokyo, Sect. I A,28, 415–437 (1981)Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Jeffrey Hoffstein
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

Personalised recommendations