Dirichlet Series for the Group GL(N)

  • Herve Jacquet
Part of the Tata Institute of Fundamental Research Studies in Mathematics book series (TATA STUDIES)

Abstract

Suppose ϕ is a modular cusp form with Fourier expansion:
$$ \varphi \left( z \right) = \sum\limits_{n > 1} {{a_n}} \exp \left( {2i\pi nz} \right). $$
(1.1)

Keywords

Convolution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C—S] Casselman W. and J. Shalika, Unramified Whittaker functions, to appear.Google Scholar
  2. [G-K]
    Gelfand J. M. and D. A. Kazdan, Representations of GI (n, K) where K is a local field, in Lie groups and their representations, John Wiley and Sons (1975), 95–118.Google Scholar
  3. [J-S1]
    Jacquet H. and J. Shalika, Hecke theory for GL(3), Comp. Math., 29: 1 (1974), 75–87.MathSciNetMATHGoogle Scholar
  4. [J-S2]
    Jacquet H. and J. Shalika, Comparaison des representations automorphes du groupe line aire, C.R. Acad. Sc. Paris, 284 (1977), 741–744.MathSciNetMATHGoogle Scholar
  5. [J-S-PI]
    Jacquet H., J. Shalika, and J. J. Piatetski-Shaprio, Automorphic forms on GL(3), I and II Annals of Math, 109 (1979).Google Scholar
  6. J-S-P2] Jacquet H., J. Shalika, and J. J. Piatetski Shapiro, Facteurs L et e du groupe lineaire, to appear in C.R. Acad. Sci. (1979), Paris.Google Scholar
  7. J—S—P3] JACQUET H., J. Shalika, and J. J. Piatetski-Shapiro, Constructions of cusp forms on GL(n), Univ. of Maryland, Lectures Notes in Math. 16 (1975).Google Scholar
  8. PI] Piatetski-Shapiro J.J., Euler subgroups,in Lie groups and their representations, John Wiley and Sons (1975), 597–620.Google Scholar
  9. P2] Piatetski-Shapiro J.J., Zeta functions on GL(n), Mimeographed notes, Univ. of Maryland.Google Scholar
  10. Sha], Shalika J., The multiplicity one theorem for GL(n), Annals of Math. 100 (1974), 171–193.CrossRefGoogle Scholar
  11. Shi], Shintani T., On an explicit formula for class-1 “Whittaker functions” on GL over p-adic fields, Proc. Japan. Acad. 52 (1976), 180–182.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Herve Jacquet

There are no affiliations available

Personalised recommendations