Meromorphic continuation of Selberg zeta functions with twists having non-expanding cusp monodromy

被引：10

作者：

Fedosova, Ksenia ^{[1
]}

Pohl, Anke ^{[2
]}

机构：

[1] Albert Ludwigs Univ Freiburg, Math Inst, Eckerstr 1, D-79104 Freiburg, Germany

[2] Univ Bremen, Dept Math 3, Bibliothekstr 5, D-28359 Bremen, Germany

来源：

SELECTA MATHEMATICA-NEW SERIES | 2020年 / 26卷 / 01期

关键词：

Selberg zeta function; Meromorphic continuation; Non-unitary representation; Non-expanding cusp monodromy; Thermodynamic formalism; Transfer operator; VALUED MODULAR-FORMS; HECKE TRIANGLE GROUPS; SYMBOLIC DYNAMICS; THERMODYNAMIC FORMALISM; RUELLE; SERIES;

D O I：

10.1007/s00029-019-0534-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：55

共 22 条

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Ksenia Fedosova
Anke Pohl
[J]. Selecta Mathematica, 2020, 26
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Pohl, Anke
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