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
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复杂双曲空间上框架流的自守形式和动力学的生成集
DOI：
10.1017/s0143385701001511
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发表时间：
1999
影响因子：
0.9
通讯作者：
S. Katok
中科院分区：
文献类型：
--
作者：
T. Foth;S. Katok
设G是不含紧因子的半单李群，K是G的极大紧子群，\Gamma是G中的格.我们研究\Gamma的自守形式，如果G是真实的秩1与一些额外的假设，使用动力学方法的基础上的性质的齐次流\Gamma\反斜杠G和Livshitz型定理，我们证明了这样的流。在Hermitian情形G=SU（n，1）下，对K的一维表示构造了与\Gamma\反斜杠G/K上的闭测地线相关联的相对Poincaré级数，并证明了它们跨越了相应的全纯尖点型空间.
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 a 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 Poincaré 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 holomorphic cusp forms.