Trace Formulae, Zeta Functions, Congruences and Reidemeister Torsion in Nielsen Theory
| dc.creator | Fel'shtyn, Alexander | |
| dc.creator | Hill, Richard | |
| dc.date | 1998-02-04 | |
| dc.date.accessioned | 2026-07-07T05:23:45Z | |
| dc.date.available | 2026-07-07T05:23:45Z | |
| dc.description | In this paper we prove trace formulae for the Reidemeister number of a group endomorphism. This result implies the rationality of the Reidemeister zeta function in the following cases: the group is a direct product of a finite group and a finitely generated Abelian group; the group is finitely generated, nilpotent and torsion free. We continue to study analytical properties of the Nielsen zeta function. We connect the Reidemeister zeta function of an endomorphism of a direct product of a finite group and a finitely generated free Abelian group with the Lefschetz zeta function of the induced map on the unitary dual of the group. As a consequence we obtain a relation between a special value of the Reidemeister zeta function and a certain Reidemeister torsion. We also prove congruences for Reidemeister numbers of iterates of an endomorphism of a direct product of a finite group and a finitely generated free Abelian group which are the same as those found by Dold for Lefschetz numbers. | |
| dc.description | 21 pages, LATeX, 86 KB, no figures | |
| dc.identifier | https://arxiv.org/abs/math/9802017 | |
| dc.identifier | http://arxiv.org/abs/math/9802017 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76569 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 58F20; 55M20, 57Q10 | |
| dc.title | Trace Formulae, Zeta Functions, Congruences and Reidemeister Torsion in Nielsen Theory | |
| dc.type | text |