Analytic torsion, dynamical zeta functions, and the Fried conjecture

Abstract

We prove the equality of the analytic torsion and the value at zero of a Ruelle dynamical zeta function associated with an acyclic unitarily flat vector bundle on a closed locally symmetric reductive manifold. This solves a conjecture of Fried. This article should be read in conjunction with an earlier paper by Moscovici and Stanton.

Published version, 74 pages

References in corpus (2)

• Exponential Estimate for the asymptotics of Bergman kernels
• Ruelle zeta function at zero for surfaces

Cited by in corpus (15)

• Fried conjecture in small dimensions
• Pollicott-Ruelle resonant states and Betti numbers
• The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds
• Flat vector bundles and analytic torsion on orbifolds
• Twisted Ruelle zeta function at zero for compact hyperbolic surfaces
• Dynamical torsion for contact Anosov flows
• Analytic torsion, dynamical zeta function, and the Fried conjecture for admissible twists
• On Fried's conjecture for compact hyperbolic manifolds
• Morse-Smale flow, Milnor metric, and dynamical zeta function
• Geometric hypoelliptic Laplacian and orbital integrals (after Bismut, Lebeau and Shen)
• Ruelle zeta function from field theory
• On full asymptotics of analytic torsions for compact locally symmetric orbifolds
• The twisted Ruelle zeta function on compact hyperbolic orbisurfaces and Reidemeister-Turaev torsion
• Dynamical zeta functions for geodesic flows and the higher-dimensional Reidemeister torsion for Fuchsian groups
• Hypoelliptic Laplacian and twisted trace formula