Rationality of twist representation zeta functions of compact p-adic analytic groups
File(s)
Accepted version
Author(s)
Stasinski, Alexander
Zordan, Michele
Type
Journal Article
Abstract
We prove that for any twist rigid compact p-adic analytic group G, its twist 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. Mero-morphic continuation and rationality of the abscissa of the zeta function follow
as corollaries. If G is moreover a pro-p group, we prove that its twist representation zeta function is rational in p−s. To establish these results we develop a Clifford theory for twist isoclasses of representations, including a new cohomological invariant of a twist isoclass.
as corollaries. If G is moreover a pro-p group, we prove that its twist representation zeta function is rational in p−s. To establish these results we develop a Clifford theory for twist isoclasses of representations, including a new cohomological invariant of a twist isoclass.
Date Issued
2024-11-01
Date Acceptance
2024-04-08
Citation
Transactions of the American Mathematical Society, 2024, 377 (11), pp.7601-7631
ISSN
0002-9947
Publisher
American Mathematical Society
Start Page
7601
End Page
7631
Journal / Book Title
Transactions of the American Mathematical Society
Volume
377
Issue
11
Copyright Statement
Copyright © 2024 American Mathematical Society. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Identifier
https://www.ams.org/journals/tran/0000-000-00/S0002-9947-2024-09210-3/
Publication Status
Published
Date Publish Online
2024-08-30