Analytic Torsion, Dynamical Zeta Function, and the Fried Conjecture for Admissible Twists

Abstract

We show an equality between the analytic torsion and the absolute value at zero of the Ruelle dynamical zeta function on a closed odd dimensional locally symmetric space twisted by an acyclic flat vector bundle obtained by the restriction of a representation of the underlying Lie group. This generalises author’s previous result for unitarily flat vector bundles, and the results of Bröcker, Müller, and Wotzke on closed hyperbolic manifolds.