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Twisted Ruelle zeta function at zero for compact hyperbolic surfaces

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Let X be an orientable compact connected hyperbolic surface of genus g. In this paper, we prove that the twisted Selberg and Ruelle zeta functions, associated with an arbitrary finite-dimensional complex representation χ of π 1(X) admit a meromorphic continuation to C. Moreover, we study the behavior of the twisted Ruelle zeta function at s=0 and prove that at this point it has a zero of order dim⁡(χ)(2g−2).

OriginalsprogEngelsk
TidsskriftJournal of Number Theory
Vol/bind243
Sider (fra-til)38-61
Antal sider24
ISSN0022-314X
DOI
StatusUdgivet - feb. 2023

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