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

Tatyana Foth, Svetlana Katok

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Abstract

Let G be a semisimple Lie group with no compact factors, K a maximal compact subgroup of G, and Γ a lattice in G. We study automorphic forms for Γ if G is of real rank one with some additional assumptions, using a dynamical approach based on properties of the homogeneous flow on Γ\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 geodesies on Γ\G/K for one-dimensional representations of K, and prove that they span the corresponding spaces of holomorphic cusp forms.

Original languageEnglish (US)
Pages (from-to)1071-1099
Number of pages29
JournalErgodic Theory and Dynamical Systems
Volume21
Issue number4
DOIs
StatePublished - Aug 1 2001

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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