复双曲空间上自守形式的生成集与框架流的动力学
Spanning sets for automorphic forms and dynamics of the frame flow on complex hyperbolic spaces
摘要：
设G是不含紧因子的半单李群，K是G的极大紧子群，$Γ$是G中的格.利用基于$Γ\backslash G$上齐次流性质的动力学方法和证明的一个Livshitz型定理，研究了当G为实秩1时$Γ$的自守形式.在Hermitian情形G=SU（n，1）下，对K的一维表示构造了与$Γ\backslash G/K$上的闭测地线相关联的相对Poincare级数，并证明了它们跨越相应的尖点形式空间.
英文摘要：
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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