%0 Journal Article
%T Spanning sets for automorphic forms and dynamics of the frame flow on complex hyperbolic spaces
%A Tatyana Foth
%A Svetlana Katok
%J Mathematics
%D 1999
%I arXiv
%X 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 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 Poincare 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 cusp forms.
%U http://arxiv.org/abs/math/9911046v3