Analytic torsion for arithmetic locally symmetric manifolds and approximation of L2-torsion

Jasmin Matz*, Werner Müller

*Corresponding author for this work

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Abstract

In this paper we define a regularized version of the analytic torsion for quotients of a symmetric space of non-positive curvature by arithmetic lattices. 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 kernel. Then we study the limiting behavior of the analytic torsion as the lattices run through a sequence of congruence subgroups of a fixed arithmetic subgroup. Our main result states that for sequences of principal congruence subgroups, which converge to 1 at a fixed finite set of places and strongly acyclic flat bundles, the logarithm of the analytic torsion, divided by the index of the subgroup, converges to the L2-analytic torsion.

Original languageEnglish
Article number109727
JournalJournal of Functional Analysis
Volume284
Issue number1
Number of pages67
ISSN0022-1236
DOIs
Publication statusPublished - 2023

Bibliographical note

Publisher Copyright:
© 2022 The Author(s)

Keywords

  • Analytic torsion
  • Locally symmetric spaces

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