PRO-ISOMORPHIC ZETA FUNCTIONS OF NILPOTENT GROUPS AND LIE RINGS UNDER BASE EXTENSION

Mark N. Berman, Itay Glazer, Michael M. Schein

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We consider pro-isomorphic zeta functions of the groups γ(OK), where γ is a unipotent group scheme defined over Z and K varies over all number fields. Under certain conditions, we show that these functions have a fine Euler decomposition with factors indexed by primes p of K and depending only on the structure of γ, the degree [K : Q], and the cardinality of the residue field OK/p. We show that the factors satisfy a certain uniform rationality and study their dependence on [K : Q]. Explicit computations are given for several families of unipotent groups.

Original languageEnglish
Pages (from-to)1051-1100
Number of pages50
JournalTransactions of the American Mathematical Society
Volume375
Issue number2
DOIs
StatePublished - 2022

Bibliographical note

Publisher Copyright:
© 2022 American Mathematical Society. All rights reserved.

Funding

Received by the editors July 9, 2020, and, in revised form, March 22, 2021, May 19, 2021, and May 30, 2021. 2020 Mathematics Subject Classification. Primary 11M41, 20E07. The third author was supported by grant 1246/2014 from the German-Israeli Foundation for Scientific Research and Development.

FundersFunder number
German-Israeli Foundation for Scientific Research and Development

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