Hiroshima Mathematical Journal

Zeta function of Selberg's type for compact quotient of ${\rm SU}(n,1)\;(n\geq 2)$

Masato Wakayama

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Hiroshima Math. J. Volume 14, Number 3 (1985), 597-618.

First available in Project Euclid: 21 March 2008

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Primary: 11F55: Other groups and their modular and automorphic forms (several variables)
Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields 22E45: Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05}


Wakayama, Masato. Zeta function of Selberg's type for compact quotient of ${\rm SU}(n,1)\;(n\geq 2)$. Hiroshima Math. J. 14 (1985), no. 3, 597--618.https://projecteuclid.org/euclid.hmj/1206132940

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  • [1] Gangolli, R.: On the lenth spectra of certain compact manifolds of negative curvature.J. Differential Geom. 12,403-423 (1977).
  • [2] Gangolli, R.: Zeta functions of Selberg's type for compact space forms of symmetric spaces of rank one. Illinois J. Math. 21,1-41 (1977).
  • [3] Gangolli, R., Warner, G.: On Selberg's trace formula. J. Math. Soc.Japan 27, 328-343 (1973).
  • [4] Harish-Chandra: Discrete series for semisimple Lie groups, II. Acta Math. 116, 1--111 (1966).
  • [5] Knapp, A. W., Okamoto, K.: Limits of holomorphic discrete series. J. Functional Analysis 9, 375-409(1972).
  • [6] Knapp, A. W., Stein, E. M.: Intertwining operators for semisimple groups, II. Invent. Math. 60,9-84 (1980).
  • [7] Muta, Y.: On the spherical functions with one dimensional iC-types and Paley-Wiener type theorem onsome simple Lie groups. Rep. Sci. andEngin. Saga Univ. 9,31-59(1981).
  • [8] Sally, Jr.,P.J.,Warner, G.: The Fourier transform of invariant distributions. "Lecture Note in Math." Vol. 266,297-320, Springer Verlag, Berlin/New York,1971.
  • [9] Scott, D.: Selberg type zeta functions for thegroup of complex two by two matrices of determinant one. Math. Ann.253,177-194 (1980).
  • [10] Selberg, A.: Harmonic analysis anddiscontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series. J. Indian Math. Soc.20, 47-87 (1956).
  • [11] Trombi, P.C : Harmonic analysis of C P (G, F) (l<p<2). J. Functional Analysis 40, 84-125 (1981).
  • [12] Wakayama, M.: Zeta functions of Selberg's type associated with homogeneous vector bundles, (to appear).
  • [13] Wallach, N.R.: An asymptotic formula of Gelfand and Gangolli for the spectrum of \G. J. Differential Geom. 11,91-101 (1976).
  • [14] Wallach, N.R.: On the Selberg trace formula in the case of compact quotient. Bull. Amer. Math. Soc. 82, 171-195 (1976).
  • [J5] Warner, G.: Harmonic analysis onsemisimple Liegroups I,II. Springer Verlag, Berlin/ New York,1972.