Fel'shtyn, Alexander and Klopsch, Benjamin (2021) Pólya-Carlson dichotomy for coincidence Reidemeister zeta functions via profinite completions. MPIM Preprint Series 2021 (8).
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Abstract
We consider coincidence Reidemeister zeta functions for tame endomorphism pairs of nilpotent groups of finite rank, shedding new light on the subject by means of profinite completion techniques. In particular, we provide a closed formula for coincidence Reidemeister numbers for iterations of endomorphism pairs of torsion-free nilpotent groups of finite rank, based on a weak commutativity condition, which derives from simultaneous triangularisability on abelian sections. Furthermore, we present results in support of a Pólya-Carlson dichotomy between rationality and a natural boundary for the analytic behaviour of the zeta functions in question.
| Item Type: | MPIM Preprint |
|---|---|
| Subjects: | 2 Analysis > 37-XX Dynamical systems and ergodic theory |
| Divisions: | Research > Preprints |
| Depositing User: | Andrea Kohlhuber |
| Date Deposited: | 31 Mar 2021 09:38 |
| Last Modified: | 18 May 2021 11:11 |
| URI: | https://archive.mpim-bonn.mpg.de/id/eprint/4526 |
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