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 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 Bröcker, Müller, and Wotzke on closed hyperbolic manifolds.

40 pages. arXiv admin note: text overlap with arXiv:2009.03427

References in corpus (4)

• The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds
• Dynamical Zeta Functions in the Nonorientable Case
• On Fried's conjecture for compact hyperbolic manifolds
• Complex valued analytic torsion and dynamical zeta function on locally symmetric spaces

Cited by in corpus (3)

• Twisted Ruelle zeta function at zero for compact hyperbolic surfaces
• The twisted Ruelle zeta function on compact hyperbolic orbisurfaces and Reidemeister-Turaev torsion
• Resolvent of vector fields and Lefschetz numbers