Analytic torsion, dynamical zeta functions, and the Fried conjecture
type: Item
instance of: scholarly article
title: Analytic torsion, dynamical zeta functions, and the Fried conjecture
zbMATH Open document ID: 1378.58022
author: Shu Shen
published in: Analysis \& PDE
publication date: 2017-10-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/1602.00664
review text: In this interesting article, the author proves 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, which completes a gap in the proof given by \textit{H. Moscovici} and \textit{R. J. Stanton} [Invent. Math. 105, No. 1, 185--216 (1991; Zbl 0789.58073)] and solves a conjecture of \textit{D. Fried} [Invent. Math. 84, 523--540 (1986; Zbl 0621.53035)].
reviewed by: Yong Wang
Mathematics Subject Classification ID: 58J20
Mathematics Subject Classification ID: 58J52
Mathematics Subject Classification ID: 11F72
Mathematics Subject Classification ID: 11M36
Mathematics Subject Classification ID: 37C30
zbMATH DE Number: 6789258
zbMATH Keywords: index theory and related fixed point theorems
zbMATH Keywords: analytic torsion
zbMATH Keywords: Selberg trace formula
zbMATH Keywords: dynamical zeta functions
Wikidata QID: Q123089692
MaRDI profile type: Publication
OpenAlex ID: W2759110294
arXiv ID: 1602.00664
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DOI: 10.2140/APDE.2018.11.1
description: scientific article