1999/11/08 by Tatyana Foth, Svetlana Katok, Foth, Tatyana +1
Mathematics · #32N15 #Advanced Algebra and Geometry #Complex Variables (math.CV) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #math.CV #math.DG #math.DS #msc:32N15
paper · pdf · doi:10.48550/arxiv.math/9911046
33 pages, 1 figure; accepted for publication in "Ergodic Theory and Dynamical Systems"; final version
openalex publication_date 1999/11/08 · arxiv created 2000/03/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.