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Spanning sets for automorphic forms and dynamics of the frame flow on complex hyperbolic spaces

Published online by Cambridge University Press:  06 August 2001

TATYANA FOTH  and
SVETLANA KATOK
TATYANA FOTH
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA (e-mail: [email protected])
SVETLANA KATOK
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA (e-mail: [email protected])
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Abstract

Let G be a semisimple Lie group with no compact factors, K a maximal compact subgroup of G, and \Gamma a lattice in G. We study automorphic forms for \Gamma if G is of real rank one with some additional assumptions, using a dynamical approach based on properties of the homogeneous flow on \Gamma\backslash G and a Livshitz type theorem we prove for such a flow. In the Hermitian case G=SU(n,1) we construct relative Poincaré series associated to closed geodesics on \Gamma\backslash G/K for one-dimensional representations of K, and prove that they span the corresponding spaces of holomorphic cusp forms.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 4 , August 2001 , pp. 1071 - 1099
Copyright
2001 Cambridge University Press

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