Author:
Fedosova Ksenia,Pohl Anke
Abstract
AbstractWe initiate the study of Selberg zeta functions $$Z_{\Gamma ,\chi }$$ZΓ,χ for geometrically finite Fuchsian groups $$\Gamma $$Γ and finite-dimensional representations $$\chi $$χ with non-expanding cusp monodromy. We show that for all choices of $$(\Gamma ,\chi )$$(Γ,χ), the Selberg zeta function $$Z_{\Gamma ,\chi }$$ZΓ,χ converges on some half-plane in $$\mathbb {C}$$C. In addition, under the assumption that $$\Gamma $$Γ admits a strict transfer operator approach, we show that $$Z_{\Gamma ,\chi }$$ZΓ,χ extends meromorphically to all of $$\mathbb {C}$$C.
Publisher
Springer Science and Business Media LLC
Subject
General Physics and Astronomy,General Mathematics
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