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Geometric and Functional Analysis

, Volume 27, Issue 6, pp 1378–1449 | Cite as

Analytic torsion of arithmetic quotients of the symmetric space \({\rm SL} (n,\mathbb{R})/ {\rm SO}(n)\)

  • Jasmin Matz
  • Werner Müller
Article

Abstract

In this paper we define a regularized version of the analytic torsion for arithmetic quotients of the symmetric space \({{\rm SL}(n,\mathbb{R})/ {\rm SO}(n)}\). The definition is based on the study of the renormalized trace of the corresponding heat operators, which is defined as the geometric side of the Arthur trace formula applied to the heat operator.

Keywords and phrases

Analytic torsion Locally symmetric spaces 

Mathematics Subject Classification

Primary: 58J52 Secondary: 11M36 

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Authors and Affiliations

  1. 1.Einstein Institute of MathematicsHebrew University of JerusalemJerusalemIsrael
  2. 2.Mathematisches InstitutUniversität BonnBonnGermany

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