Period functions for Hecke triangle groups, and the Selberg zeta function as a Fredholm determinant
Period functions for Hecke triangle groups, and the Selberg zeta function as a Fredholm determinant
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Hecke 三角形群的周期函数和作为 Fredholm 行列式的 Selberg zeta 函数
DOI：
10.1017/s0143385711000794
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发表时间：
2011
影响因子：
0.9
通讯作者：
A. Pohl
中科院分区：
文献类型：
--
作者：
Martin Möller;A. Pohl
摘要我们将任何上有限Hecke三角形群的Maass尖点型刻画为转移算子族的适当正则性的1-本征函数。这个传递算子家族与作为双曲平面上的Hecke三角形群的作用的轨道空间而产生的轨道上的测地线流的某种符号动力学相关联。此外，我们表明，Selberg zeta函数是Fredholm行列式的转移算子家庭与加速这一象征性的动态。
Abstract We characterize Maass cusp forms for any cofinite Hecke triangle group as 1-eigenfunctions of appropriate regularity of a transfer operator family. This transfer operator family is associated to a certain symbolic dynamics for the geodesic flow on the orbifold arising as the orbit space of the action of the Hecke triangle group on the hyperbolic plane. Moreover, we show that the Selberg zeta function is the Fredholm determinant of the transfer operator family associated to an acceleration of this symbolic dynamics.