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2020 Dynamical zeta functions of Reidemeister type
Alexander Fel'shtyn, Malwina Ziętek
Topol. Methods Nonlinear Anal. 56(2): 433-455 (2020). DOI: 10.12775/TMNA.2020.023

Abstract

In this paper we study dynamical representation theory zeta functions counting numbers of fixed irreducible representations for iterations of group endomorphism. The rationality and functional equation for these zeta functions are proven for several classes of groups. We prove Pólya-Carlson dichotomy between rationality and a natural boundary for analytic behavior of the Reidemeister zeta functions for a large class of automorphisms of infinitely generated Abelian groups. We also establish the connection between the Reidemeister zeta function and dynamical representation theory zeta functions under restriction of endomorphism to a subgroup.

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Alexander Fel'shtyn. Malwina Ziętek. "Dynamical zeta functions of Reidemeister type." Topol. Methods Nonlinear Anal. 56 (2) 433 - 455, 2020. https://doi.org/10.12775/TMNA.2020.023

Information

Published: 2020
First available in Project Euclid: 5 December 2020

Digital Object Identifier: 10.12775/TMNA.2020.023

Rights: Copyright © 2020 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.56 • No. 2 • 2020
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