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 language | English |
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Pages (from-to) | 1051-1100 |
Number of pages | 50 |
Journal | Transactions of the American Mathematical Society |
Volume | 375 |
Issue number | 2 |
DOIs | |
State | Published - 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.
Funders | Funder number |
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German-Israeli Foundation for Scientific Research and Development |