Pólya-Carlson dichotomy for coincidence Reidemeister zeta functions via profinite completions

DOI10.1016/j.indag.2022.02.004OpenAlexW3132431331MaRDI QIDQ2673081

Alexander Fel'shtyn, Benjamin Klopsch

Publication date: 9 June 2022

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.10900

zbMATH Keywords

twisted conjugacy classesReidemeister zeta functionabelian group of finite ranknilpotent group of finite rank

Mathematics Subject Classification ID

Nilpotent groups (20F18) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Finite nilpotent groups, (p)-groups (20D15) Residual properties and generalizations; residually finite groups (20E26) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30) Limits, profinite groups (20E18)

Related Items (1)

Rank-two solenoidal endomorphisms

Cites Work

• Nielsen zeta functions for maps on infra-nilmanifolds are rational
• Twisted conjugacy classes in nilpotent groups.
• The Reidemeister zeta function with applications to Nielsen theory and a connection with Reidemeister torsion
• Dynamics on abelian varieties in positive characteristic
• New zeta functions of Reidemeister type and the twisted Burnside-Frobenius theory
• Towards a Pólya-Carlson dichotomy for algebraic dynamics
• The Nielsen and Reidemeister numbers of maps on infra-solvmanifolds of type \((\mathrm{R})\)
• Synchronization points and associated dynamical invariants
• Dynamical zeta functions of Reidemeister type and representations spaces
• Periodic points of endomorphisms on solenoids and related groups
• The Reidemeister zeta function and the computation of the Nielsen zeta function
• Dynamical zeta functions, Nielsen theory and Reidemeister torsion
• Reidemeister zeta functions of low-dimensional almost-crystallographic groups are rational
• Varieties of groups
• Some Theorems on Commutative Matrices
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