Duke Mathematical Journal

Bounds for multiplicities of automorphic representations

Peter Sarnak and Xiaoxi Xue

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 64, Number 1 (1991), 207-227.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077295393

Digital Object Identifier
doi:10.1215/S0012-7094-91-06410-0

Mathematical Reviews number (MathSciNet)
MR1131400

Zentralblatt MATH identifier
0741.22010

Subjects
Primary: 22E45: Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05}
Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields 11F72: Spectral theory; Selberg trace formula 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]

Citation

Sarnak, Peter; Xue, Xiaoxi. Bounds for multiplicities of automorphic representations. Duke Math. J. 64 (1991), no. 1, 207--227. doi:10.1215/S0012-7094-91-06410-0. https://projecteuclid.org/euclid.dmj/1077295393


Export citation

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.
  • [B-HC] A. Borel and Harish-Chandra, Arithmetic subgroups of algebraic groups, Ann. of Math. (2) 75 (1962), 485–535.
  • [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.
  • [D-R-S] W. Duke, Z. Rudnick, and P. Sarnak, The density of integral points on affine homogeneous varieties, preprint.
  • [D-W]1 David L. de George and Nolan R. Wallach, Limit formulas for multiplicities in $L\sp2(\Gamma \backslash G)$, Ann. Math. (2) 107 (1978), no. 1, 133–150.
  • [D-W]2 D. DeGeorge and N. Wallach, Limit formulas for multiplicities in $L\sp2(\Gamma \backslash G)$. II. The tempered spectrum, Ann. of Math. (2) 109 (1979), no. 3, 477–495.
  • [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].
  • [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.
  • [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.
  • [Kna] A. Knapp, Representation theory of semisimple groups, Princeton Mathematical Series, vol. 36, Princeton University Press, Princeton, NJ, 1986.
  • [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.
  • [Rd] B. Randol, Small eigenvalues of the Laplace operator on compact Riemann surfaces, Bull. Amer. Math. Soc. 80 (1974), 996–1000.
  • [S] P. Sarnak, Diophantine problems and linear groups, to appear in Proc. Internat. Cong. Math., Kyoto, Japan, 1990.
  • [Sc] W. Scharlau, Quadratic and Hermitian forms, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 270, Springer-Verlag, Berlin, 1985.
  • [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.
  • [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.
  • [X1] X. Xue, On the first Betti numbers of hyperbolic surfaces, Duke Math. J. 64 (1991), no. 1, 85–110.
  • [X2] X. Xue, On the Betti numbers of hyperbolic manifolds, submitted, 1991.