TY - JOUR
T1 - Spanning sets for automorphic forms and dynamics of the frame flow on complex hyperbolic spaces
AU - Foth, Tatyana
AU - Katok, Svetlana
PY - 2001/8
Y1 - 2001/8
N2 - 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.
AB - 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.
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U2 - 10.1017/S0143385701001511
DO - 10.1017/S0143385701001511
M3 - Article
AN - SCOPUS:0040927489
SN - 0143-3857
VL - 21
SP - 1071
EP - 1099
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 4
ER -