The twisted Selberg trace formula and the Selberg zeta function for compact orbifolds

Abstract

We study elements of the spectral theory of compact hyperbolic orbifolds $\Gamma \backslash {\mathbb{H}}^n$. We establish a version of the Selberg trace formula for non-unitary representations of $\Gamma$ and prove that the associated Selberg zeta function admits a meromorphic continuation to $\mathbb{C}$.

arXiv admin note: text overlap with arXiv:0906.3997 by other authors

References in corpus (2)

• On the asymptotics of the analytic torsion for compact hyperbolic orbifolds
• Ruelle and Selberg zeta functions for non-unitary twists

Cited by in corpus (4)

• On the asymptotics of the analytic torsion for compact hyperbolic orbifolds
• The twisted Ruelle zeta function on compact hyperbolic orbisurfaces and Reidemeister-Turaev torsion
• Hypoelliptic Laplacian and twisted trace formula
• Analytic torsion of finite volume hyperbolic orbifolds