Duke Mathematical Journal

On explicit integral formulas for $GL(n,\mathbb{R})$-Whittaker functions

Eric Stade

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J. Volume 60, Number 2 (1990), 313-362.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077297295

Mathematical Reviews number (MathSciNet)
MR1047756

Zentralblatt MATH identifier
0731.11027

Digital Object Identifier
doi:10.1215/S0012-7094-90-06013-2

Subjects
Primary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields
Secondary: 22E30: Analysis on real and complex Lie groups [See also 33C80, 43-XX] 33C80: Connections with groups and algebras, and related topics

Citation

Stade, Eric. On explicit integral formulas for G L ( n , ℝ ) -Whittaker functions. Duke Math. J. 60 (1990), no. 2, 313--362. doi:10.1215/S0012-7094-90-06013-2. http://projecteuclid.org/euclid.dmj/1077297295.


Export citation

References

  • [1] D. Bump, Automorphic Forms on $\mathrm GL(3,\mathbbR)$, Springer Lecture Notes in Mathematics, vol. 1083, Springer-Verlag, Berlin, 1984.
  • [2] D. Bump, The Rankin-Selberg method: A survey, to appear in the proceedings of the Selberg Symposium, Oslo, 1987.
  • [3] D. Bump, Barnes' second lemma and its application to Rankin-Selberg convolutions, to appear in Amer. J. Math.
  • [4] D. Bump and S. Friedberg, The exterior square automorphic $L$-functions on $GL(n)$, to appear.
  • [5] D. Bump and J. Huntley, in preparation.
  • [6] I. Gradshteyn and I. Ryzhik, Table of Integrals, Series, and Products, Academic Press, New York, 1980, corrected and enlarged edition.
  • [7] H. Jacquet, Fonctions de Whittaker associées aux groupes de Chevalley, Bull. Soc. Math. France 95 (1967), 243–309.
  • [8] B. Kostant, On Whittaker vectors and representation theory, Invent. Math. 48 (1978), no. 2, 101–184.
  • [9] I. I. Pjateckij-Šapiro, Euler subgroups, Lie Groups and their Representations (Proc. Summer School, Bolyai János Math. Soc., Budapest, 1971), Halsted, New York, 1975, pp. 597–620.
  • [10] A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. 20 (1956), 47–87.
  • [11] J. Shalika, The multiplicity one theorem for $\rm GL\sbn$, Ann. of Math. (2) 100 (1974), 171–193.
  • [12] E. Stade, Poincaré series for $\rm GL(3,\bf R)$-Whittaker functions, Duke Math. J. 58 (1989), no. 3, 695–729.
  • [13] I. Vinogradov and L. Takhtadzhyan, Theory of Eisenstein Series for the group $\mathrmSL(3,\mathbbR)$ and its application to a binary problem, J. Soviet Math. 18 (1982), 293–324.