# Wydawnictwa / Banach Center Publications / Wszystkie tomy

## Dynamical zeta functions, congruences in Nielsen theory and Reidemeister torsion

### Tom 49 / 1999

Banach Center Publications 49 (1999), 77-116 DOI: 10.4064/-49-1-77-116

#### Streszczenie

In this paper we prove trace formulas for the Reidemeister numbers of group endomorphisms and the rationality of the Reidemeister zeta function in the following cases: the group is finitely generated and the endomorphism is eventually commutative; the group is finite; the group is a direct sum of a finite group and a finitely generated free Abelian group; the group is finitely generated, nilpotent and torsion free. We connect the Reidemeister zeta function of an endomorphism of a direct sum of a finite group and a finitely generated free Abelian group with the Lefschetz zeta function of the unitary dual map, and as a consequence obtain a connection of the Reidemeister zeta function with Reidemeister torsion. We also prove congruences for Reidemeister numbers which are the same as those found by Dold for Lefschetz numbers.

#### Autorzy

• Alexander Fel'shtyn
• Richard Hill

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