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Zeta function of representations of compact $p$-adic analytic groups


Author: A. Jaikin-Zapirain
Journal: J. Amer. Math. Soc. 19 (2006), 91-118
MSC (2000): Primary 20E18; Secondary 20C15, 20G25, 22E35
DOI: https://doi.org/10.1090/S0894-0347-05-00501-1
Published electronically: September 7, 2005
MathSciNet review: 2169043
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Abstract: Let $G$ be an FAb compact $p$-adic analytic group and suppose that $p>2$ or $p=2$ and $G$ is uniform. We prove that there are natural numbers $n_1, \ldots , n_k$ and functions $f_1(p^{-s}),\ldots , f_k(p^{-s})$ rational in $p^{-s}$ such that \[ \zeta ^G(s)=\sum _{\lambda \in \operatorname {Irr}(G)} \lambda (1) ^{-s}=\sum _{i=1}^kn_i^{-s}f_i(p^{-s}).\]


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Additional Information

A. Jaikin-Zapirain
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain
MR Author ID: 646902
Email: andrei.jaikin@uam.es

Keywords: Profinite groups, zeta functions, representations
Received by editor(s): June 2, 2004
Published electronically: September 7, 2005
Additional Notes: This work has been supported by the FEDER, MEC Grant MTM2004-04665, and the Ramón y Cajal Program
Article copyright: © Copyright 2005 American Mathematical Society