# Dynamical zeta functions for geodesic flows and the higher-dimensional Reidemeister torsion for Fuchsian groups

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## 抄録

We show that the absolute value at zero of the Ruelle zeta function defined by the geodesic flow coincides with the higher-dimensional Reidemeister torsion for the unit tangent bundle over a 2-dimensional hyperbolic orbifold and a non-unitary representation of the fundamental group. Our proof is based on the integral expression of the Ruelle zeta function. This integral expression is derived from the functional equation of the Selberg zeta function for a discrete subgroup with elliptic elements in PSL2(R). We also show that the asymptotic behavior of the higher-dimensional Reidemeister torsion is determined by the contribution of the identity element to the integral expression of the Ruelle zeta function.

本文言語 English 155-176 22 Journal fur die Reine und Angewandte Mathematik 2022 784 https://doi.org/10.1515/crelle-2021-0075 Published - 2022 3月 1 はい

• 数学 (全般)
• 応用数学

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