## Duke Mathematical Journal

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

#### Article information

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

Dates
First available in Project Euclid: 20 February 2004

https://projecteuclid.org/euclid.dmj/1077297295

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

Mathematical Reviews number (MathSciNet)
MR1047756

Zentralblatt MATH identifier
0731.11027

#### Citation

Stade, Eric. On explicit integral formulas for $GL(n,\mathbb{R})$ -Whittaker functions. Duke Math. J. 60 (1990), no. 2, 313--362. doi:10.1215/S0012-7094-90-06013-2. https://projecteuclid.org/euclid.dmj/1077297295

#### References

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• [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.