Twisted Ruelle zeta function at zero for compact hyperbolic surfaces

Jan Frahm; Polyxeni Spilioti

doi:10.1016/j.jnt.2022.08.003

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arXiv · 2105.13321

Twisted Ruelle zeta function at zero for compact hyperbolic surfaces

Jan Frahm·Polyxeni Spilioti

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Abstract

Let $X$ be a compact, hyperbolic surface of genus $g\geq 2$. In this paper, we prove that the twisted Selberg and Ruelle zeta functions, associated with an arbitrary, finite-dimensional, complex representation $\chi$ of $\pi_1(X)$ admit a meromorphic continuation to $\mathbb{C}$. Moreover, we study the behaviour of the twisted Ruelle zeta function at $s=0$ and prove that at this point, it has a zero of order $\dim(\chi)(2g-2)$.

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BibTeX RIS

Jan Frahm, Polyxeni Spilioti. 2021-05-27. Twisted Ruelle zeta function at zero for compact hyperbolic surfaces. https://doi.org/10.1016/j.jnt.2022.08.003

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