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.
@article{bwmeta1.element.bwnjournal-article-bcpv49i1p77bwm,
author = {Fel'shtyn, Alexander and Hill, Richard},
title = {Dynamical zeta functions, congruences in Nielsen theory and Reidemeister torsion},
journal = {Banach Center Publications},
volume = {50},
year = {1999},
pages = {77-116},
zbl = {0963.37019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv49i1p77bwm}
}
Fel'shtyn, Alexander; Hill, Richard. Dynamical zeta functions, congruences in Nielsen theory and Reidemeister torsion. Banach Center Publications, Tome 50 (1999) pp. 77-116. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv49i1p77bwm/
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