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Rationality of representation zeta functions of compact p-adic analytic groups

Stasinski, Alexander; Zordan, Michele

Authors

Michele Zordan



Abstract

We prove that for any FAb compact p-adic analytic group G, its representation zeta function is a finite sum of terms n −s i fi(p −s), where ni are natural numbers and fi(t) ∈ Q(t) are rational functions. Meromorphic continuation and rationality of the abscissa of the zeta function follow as corollaries. If G is moreover a prop group, we prove that its representation zeta function is rational in p −s. These results were proved by Jaikin-Zapirain for p > 2 or for G uniform and pro-2, respectively. We give a new proof which avoids the Kirillov orbit method and works for all p.

Journal Article Type Article
Acceptance Date Dec 6, 2023
Deposit Date Jun 17, 2024
Journal American Journal of Mathematics
Print ISSN 0002-9327
Publisher Johns Hopkins University Press
Peer Reviewed Peer Reviewed
Public URL https://durham-repository.worktribe.com/output/2484540
Publisher URL https://muse.jhu.edu/journal/5