Analytic torsion, dynamical zeta functions and orbital integrals

Shu Shen

doi:10.1016/j.crma.2016.01.008

Differential geometry

Analytic torsion, dynamical zeta functions and orbital integrals

Presented by: Jean-Michel Bismut

Shu Shen ¹

¹ Johann von Neumann-Haus, Rudower Chaussee 25, 12489 Berlin, Germany

Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 433-436.

Abstract
Résumé

The purpose of this Note is to prove an identity between the analytic torsion and the value at zero of a dynamical zeta function associated with an acyclic unitarily flat vector bundle on a closed locally symmetric reductive manifold, which solves a conjecture of Fried.

L'objet de cette Note est de démontrer une égalité entre la torsion analytique et la valeur en zéro d'une fonction zêta dynamique associée à un fibré vectoriel unitairement plat sur une variété compacte localement symétrique réductive. Nous démontrons aussi une conjecture de Fried.

Received: 2015-11-06
Accepted: 2016-01-21
Published online: 2016-02-10

DOI: 10.1016/j.crma.2016.01.008

Author's affiliations:

Shu Shen ¹

¹ Johann von Neumann-Haus, Rudower Chaussee 25, 12489 Berlin, Germany

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Shu Shen. Analytic torsion, dynamical zeta functions and orbital integrals. Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 433-436. doi : 10.1016/j.crma.2016.01.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.01.008/

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