Analytic torsion, dynamical zeta function, and the Fried conjecture for admissible twists

TL;DR

This paper proves a general equality linking analytic torsion and the Ruelle dynamical zeta function for certain twisted flat vector bundles on odd-dimensional locally symmetric spaces, extending previous results.

Contribution

It generalizes earlier work by establishing this equality for a broader class of admissible twists and flat bundles on symmetric spaces.

Findings

Equality between analytic torsion and zeta function at zero

Extension of previous results to more general flat bundles

Applicable to odd-dimensional locally symmetric spaces

Abstract

We show an equality between the analytic torsion and the absolute value at the zero point 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 Br\"ocker, M\"uller, and Wotzke on closed hyperbolic manifolds.