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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).

Original languageEnglish
JournalJournal of Number Theory
Pages (from-to)38-61
Number of pages24
Publication statusPublished - Feb 2023

    Research areas

  • Non-unitary representations, Selberg trace formula, Twisted Ruelle zeta function, Twisted Selberg zeta function

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