Download this article
 Download this article For screen
For printing
Recent Issues

Volume 17
Issue 5, 1501–1870
Issue 4, 1127–1500
Issue 3, 757–1126
Issue 2, 379–756
Issue 1, 1–377

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
 
Author index
To appear
 
Other MSP journals
On full asymptotics of real analytic torsions for compact locally symmetric orbifolds

Bingxiao Liu

Vol. 17 (2024), No. 4, 1261–1329
Abstract

We consider a certain sequence of flat vector bundles on a compact locally symmetric orbifold, and we evaluate explicitly the associated asymptotic Ray–Singer real analytic torsion. The basic idea is to computing the heat trace via Selberg’s trace formula, so that a key point in this paper is to evaluate the orbital integrals associated with nontrivial elliptic elements. For that purpose, we deduce a geometric localization formula, so that we can rewrite an elliptic orbital integral as a sum of certain identity orbital integrals associated with the centralizer of that elliptic element. The explicit geometric formula of Bismut for semisimple orbital integrals plays an essential role in these computations.

Keywords
real analytic torsion, orbital integral, orbifold, locally symmetric space
Mathematical Subject Classification
Primary: 11F72, 53C35, 57R18, 58C40
Milestones
Received: 25 July 2021
Revised: 16 August 2022
Accepted: 23 September 2022
Published: 17 May 2024
Authors
Bingxiao Liu
Mathematisches Institut
Universität zu Köln
Köln
Germany

Open Access made possible by participating institutions via Subscribe to Open.