Analytic torsion, dynamical zeta functions, and the Fried conjecture

Shen, Shu

doi:10.2140/apde.2018.11.1

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Analytic torsion, dynamical zeta functions, and the Fried conjecture

Shu Shen

Vol. 11 (2018), No. 1, 1–74

DOI: 10.2140/apde.2018.11.1

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.

Keywords

index theory and related fixed point theorems, analytic torsion, Selberg trace formula, dynamical zeta functions

Mathematical Subject Classification 2010

Primary: 58J20, 58J52, 11F72, 11M36, 37C30

Milestones

Received: 14 February 2016

Revised: 16 June 2017

Accepted: 17 July 2017

Published: 17 September 2017

Authors

Shu Shen
Département de Mathématique Bâtiment 425 Université Paris-Sud Orsay France

Vol. 11, No. 1, 2018