Vol. 11, No. 1, 2018

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Analytic torsion, dynamical zeta functions, and the Fried conjecture

Shu Shen

Vol. 11 (2018), No. 1, 1–74
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