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

2015/07/21 by Spilioti, Polyxeni
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1507.05947

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 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.

Related

• Twisted Dirac operators and dynamical zeta functions
• Ruelle and Selberg zeta functions for non-unitary twists
• Twisted Ruelle zeta function on hyperbolic manifolds and complex-valued analytic torsion
• Geometric zeta functions with non-unitary twists
• Dynamical zeta functions for geodesic flows and the higher-dimensional Reidemeister torsion for Fuchsian groups