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

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

1999-11-08

arxiv.org/abs/math/9911046v3

Mathematics

Complex Variables

33 pages, 1 figure; accepted for publication in "Ergodic Theory and Dynamical Systems"; final version

Scientific paper

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.

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