Meromorphic continuation of Selberg zeta functions with twists having non-expanding cusp monodromy
Meromorphic continuation of Selberg zeta functions with twists having non-expanding cusp monodromy
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DOI：
10.1007/s00029-019-0534-3
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发表时间：
2020-01-25
影响因子：
1.4
通讯作者：
Pohl, Anke
中科院分区：
文献类型：
--
作者：
Fedosova, Ksenia;Pohl, Anke
我们开始研究Selberg zeta函数Z Gamma，chi几何有限Fuchsian群Gamma和有限维表示chi与非扩展尖点单值。我们证明了对于（Gamma，chi）的所有选择，Selberg zeta函数Z Gamma，chi收敛于C中的某个半平面上.另外，在Gamma允许严格转移算子逼近的假设下，我们证明了Z Gamma，chi亚纯扩张到所有C。
We initiate the study of Selberg zeta functions Z Gamma,chi for geometrically finite Fuchsian groups Gamma and finite-dimensional representations chi with non-expanding cusp monodromy. We show that for all choices of (Gamma,chi) , the Selberg zeta function Z Gamma,chi converges on some half-plane in C . In addition, under the assumption that Gamma admits a strict transfer operator approach, we show that Z Gamma,chi extends meromorphically to all of C.