Analytic torsion, dynamical zeta functions, and the Fried conjecture

TL;DR

This paper proves the Fried conjecture by establishing the equality between analytic torsion and the value of a Ruelle dynamical zeta function at zero for certain manifolds, confirming a long-standing mathematical hypothesis.

Contribution

It provides a proof of Fried's conjecture linking analytic torsion and dynamical zeta functions on locally symmetric spaces.

Findings

Confirmed the equality of analytic torsion and zeta function value at zero.

Solved Fried's conjecture for a class of manifolds.

Connected analytic torsion with dynamical systems in a rigorous way.

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.