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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 dynamical approach based on properties of the homogeneous flow on $Γ\backslash G$ and a Livshitz type theorem we prove for such a flow. In the Hermitian case G=SU(n,1) we construct relative Poincare series associated to closed geodesics on $Γ\backslash G/K$ for one-dimensional representations of K, and prove that they span the corresponding spaces of cusp forms.

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Tatyana Foth, Svetlana Katok. 2000-03-08. Spanning sets for automorphic forms and dynamics of the frame flow on complex hyperbolic spaces. https://arxiv.org/abs/math/9911046

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