Ruelle and Selberg zeta functions for non-unitary twists

2015/06/15 by Polyxeni Spilioti, Spilioti, Polyxeni
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Random Matrices and Applications #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1506.04672

openalex publication_date 2015/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the Selberg and Ruelle zeta functions on compact hyperbolic odd dimensional manifolds. These zeta functions are defined on one complex variable s in some right half-plane of ℂ. We use the Selberg trace formula for arbitrary not neccesarily unitary representations of the fundamental group to establish the meromorphic continuation of these zeta functions to the whole complex plane.

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