Bounds for multiplicities of automorphic representations
Log in :: RSS/Atom Feeds
Duke Mathematical Journal
previous :: next

Bounds for multiplicities of automorphic representations

Peter Sarnak and Xiaoxi Xue

Source: Duke Math. J. Volume 64, Number 1 (1991), 207-227.

First Page PDF: View first page of article (PDF, 79 KB)

Primary Subjects: 22E45
Secondary Subjects: 11F70, 11F72, 22E40

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
Alternatively, the document is available for a cost of $25. Select the "buy article" button below to purchase this document from a secured VeriSign, Inc. site.
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077295393
Mathematical Reviews number (MathSciNet): MR1131400
Zentralblatt MATH identifier: 0741.22010
Digital Object Identifier: doi:10.1215/S0012-7094-91-06410-0

References

[B] A. Borel, Cohomologie de sous-groupes discrets et représentations de groupes semi-simples, Colloque “Analyse et Topologie” en l'Honneur de Henri Cartan (Orsay, 1974), Soc. Math. France, Paris, 1976, 73–112. Astérisque, No. 32-33.
Mathematical Reviews (MathSciNet): MR58:28282
Zentralblatt MATH: 0333.57023
[B-HC] A. Borel and Harish-Chandra, Arithmetic subgroups of algebraic groups, Ann. of Math. (2) 75 (1962), 485–535.
Mathematical Reviews (MathSciNet): MR26:5081
Zentralblatt MATH: 0107.14804
Digital Object Identifier: doi:10.2307/1970210
JSTOR: links.jstor.org
[B-W] A. Borel and N. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Annals of Mathematics Studies, vol. 94, Princeton University Press, Princeton, N.J., 1980.
Mathematical Reviews (MathSciNet): MR83c:22018
Zentralblatt MATH: 0443.22010
[D-R-S] W. Duke, Z. Rudnick, and P. Sarnak, The density of integral points on affine homogeneous varieties, preprint.
Mathematical Reviews (MathSciNet): MR1230289
Digital Object Identifier: doi:10.1215/S0012-7094-93-07107-4
Project Euclid: euclid.dmj/1077289840
[D-W]1 David L. de George and Nolan R. Wallach, Limit formulas for multiplicities in $L\sp{2}(\Gamma \backslash G)$, Ann. Math. (2) 107 (1978), no. 1, 133–150.
Mathematical Reviews (MathSciNet): MR58:11231
Zentralblatt MATH: 0397.22007
Digital Object Identifier: doi:10.2307/1971140
[D-W]2 D. DeGeorge and N. Wallach, Limit formulas for multiplicities in $L\sp{2}(\Gamma \backslash G)$. II. The tempered spectrum, Ann. of Math. (2) 109 (1979), no. 3, 477–495.
Mathematical Reviews (MathSciNet): MR81g:22010
Zentralblatt MATH: 0482.43006
Digital Object Identifier: doi:10.2307/1971222
JSTOR: links.jstor.org
[G-GPS] I. M. Gelfand, M. I. Graev, and N. Ya. Vilenkin, Generalized functions. Vol. 5, Academic Press [Harcourt Brace Jovanovich Publishers], New York, 1966 [1977].
Mathematical Reviews (MathSciNet): MR55:8786e
Zentralblatt MATH: 0144.17202
[Hu] M. Huxley, Exceptional eigenvalues and congruence subgroups, The Selberg trace formula and related topics (Brunswick, Maine, 1984), Contemp. Math., vol. 53, Amer. Math. Soc., Providence, RI, 1986, pp. 341–349.
Mathematical Reviews (MathSciNet): MR88d:11052
Zentralblatt MATH: 0601.10019
[Kat] J. Katznelson thesis, Stanford Univ.
[Kn] M. Kneser, Strong approximation, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965), Amer. Math. Soc., Providence, R.I., 1966, pp. 187–196.
Mathematical Reviews (MathSciNet): MR35:4225
Zentralblatt MATH: 0201.37904
[Kna] A. Knapp, Representation theory of semisimple groups, Princeton Mathematical Series, vol. 36, Princeton University Press, Princeton, NJ, 1986.
Mathematical Reviews (MathSciNet): MR87j:22022
Zentralblatt MATH: 0604.22001
[Ma] Y. Matsushima, On the first Betti number of compact quotient spaces of higher-dimensional symmetric spaces, Ann. of Math. (2) 75 (1962), 312–330.
Mathematical Reviews (MathSciNet): MR28:1629
Zentralblatt MATH: 0118.38303
Digital Object Identifier: doi:10.2307/1970176
JSTOR: links.jstor.org
[Rd] B. Randol, Small eigenvalues of the Laplace operator on compact Riemann surfaces, Bull. Amer. Math. Soc. 80 (1974), 996–1000.
Mathematical Reviews (MathSciNet): MR53:4151
Zentralblatt MATH: 0317.30017
[S] P. Sarnak, Diophantine problems and linear groups, to appear in Proc. Internat. Cong. Math., Kyoto, Japan, 1990.
Mathematical Reviews (MathSciNet): MR1159234
Zentralblatt MATH: 0743.11018
[Sc] W. Scharlau, Quadratic and Hermitian forms, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 270, Springer-Verlag, Berlin, 1985.
Mathematical Reviews (MathSciNet): MR86k:11022
Zentralblatt MATH: 0584.10010
[Se] A. Selberg, On the estimation of Fourier coefficients of modular forms, Proc. Sympos. Pure Math., Vol. VIII, Amer. Math. Soc., Providence, R.I., 1965, pp. 1–15.
Mathematical Reviews (MathSciNet): MR32:93
Zentralblatt MATH: 0142.33903
[Ti] J. Tits, Classification of algebraic semisimple groups, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965), Amer. Math. Soc.9, Providence, R.I., 1966, 1966, pp. 33–62.
Mathematical Reviews (MathSciNet): MR37:309
Zentralblatt MATH: 0238.20052
[X1] X. Xue, On the first Betti numbers of hyperbolic surfaces, Duke Math. J. 64 (1991), no. 1, 85–110.
Mathematical Reviews (MathSciNet): MR92g:22030
Zentralblatt MATH: 0741.22011
Digital Object Identifier: doi:10.1215/S0012-7094-91-06404-5
Project Euclid: euclid.dmj/1077295387
[X2] X. Xue, On the Betti numbers of hyperbolic manifolds, submitted, 1991.
previous :: next

2008 © Duke University Press