Vol. 7, No. 1, 2022

Download this article
Download this article For screen
For printing
Recent Issues
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 3
Volume 6, Issue 2
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN 2379-1691 (online)
ISSN 2379-1683 (print)
 
Author index
To appear
 
Other MSP journals
$K$-theoretic torsion and the zeta function

John R. Klein and Cary Malkiewich

Vol. 7 (2022), No. 1, 77–118
Abstract

We generalize to higher algebraic K-theory an identity (originally due to Milnor) that relates the Reidemeister torsion of an infinite cyclic cover to its Lefschetz zeta function. Our identity involves a higher torsion invariant, the endomorphism torsion, of a parametrized family of endomorphisms as well as a higher zeta function of such a family. We also exhibit several examples of families of endomorphisms having nontrivial endomorphism torsion.

Keywords
zeta function, Reidemeister torsion, $K\mkern-2mu$-theory of endomorphisms
Mathematical Subject Classification
Primary: 19J10, 57Q10
Secondary: 18F25
Milestones
Received: 23 November 2020
Revised: 8 July 2021
Accepted: 18 October 2021
Published: 20 June 2022
Authors
John R. Klein
Department of Mathematics
Wayne State University
Detroit, MI
United States
Cary Malkiewich
Department of Mathematical Sciences
Binghamton University
Binghamton, NY
United States