Selberg Zeta函数的Mayer转移算子法
Mayer Transfer Operator Approach to Selberg Zeta Function
摘要：
这些笔记基于第二作者在哥本哈根大学（2009年10月）和丹麦奥胡斯大学（2009年12月）的三次演讲。我们主要是在这里调查的结果Dieter迈耶之间的关系Selberg和Smale-Ruelle动态zeta函数。在特殊情况下，通过一个算术余有限离散群定义了双曲平面商上测地线流的动态zeta函数。更确切地说，流是为相应的单位切丛定义的。事实证明，这个群的Selberg zeta函数可以用流的经典转移算子的Fredholm行列式来表示。在一定的全纯函数空间中定义了转移算子，并给出了它在自然基中的Riemann zeta函数和Euler gamma函数的矩阵表示.
英文摘要：
These notes are based on three lectures given by the second author at Copenhagen University (October 2009) and at Aarhus University, Denmark (December 2009). We mostly present here a survey of results of Dieter Mayer on relations between Selberg and Smale-Ruelle dynamical zeta functions. In a special situation the dynamical zeta function is defined for a geodesic flow on a hyperbolic plane quotient by an arithmetic cofinite discrete group. More precisely, the flow is defined for the corresponding unit tangent bundle. It turns out that the Selberg zeta function for this group can be expressed in terms of a Fredholm determinant of a classical transfer operator of the flow. The transfer operator is defined in a certain space of holomorphic functions and its matrix representation in a natural basis is given in terms of the Riemann zeta function and the Euler gamma function.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
