Duke Mathematical Journal

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

Eric Stade

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

First available in Project Euclid: 20 February 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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  • [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.