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$K$-theoretic torsion and
the zeta function
John R. Klein and Cary Malkiewich |
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Vol. 7 (2022), No. 1, 77–118
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Abstract |
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We generalize to higher algebraic -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. |
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Keywords
zeta function, Reidemeister torsion, $K\mkern-2mu$-theory
of endomorphisms
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Mathematical Subject Classification
Primary: 19J10, 57Q10
Secondary: 18F25
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Milestones
Received: 23 November 2020
Revised: 8 July 2021
Accepted: 18 October 2021
Published: 20 June 2022
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Authors |
| John R. Klein | |
| Department of Mathematics Wayne State University Detroit, MI United States |
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| Cary Malkiewich | |
| Department of Mathematical
Sciences Binghamton University Binghamton, NY United States |
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