Functional equations of Selberg and Ruelle zeta functions for non-unitary twists

Polyxeni Spilioti

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arXiv · 1507.05947

Functional equations of Selberg and Ruelle zeta functions for non-unitary twists

Polyxeni Spilioti

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Abstract

We consider the dynamical zeta functions of Selberg and Ruelle associated with the geodesic flow on a compact odd-dimensional hyperbolic manifold. These dynamical zeta functions are defined for a complex variable $s$ in some right-half plane of $\mathbb{C}$. In [Spi18], it was proved that they admit a meromorphic continuation to the whole complex plane. In this paper, we establish functional equations for them, relating their values at $s$ with those at $-s$. We prove also a determinant representation of the zeta functions, using the regularized determinants of certain twisted differential operators.

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BibTeX RIS

Polyxeni Spilioti. 2015-07-21. Functional equations of Selberg and Ruelle zeta functions for non-unitary twists. https://arxiv.org/abs/1507.05947

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