The representation zeta function of a FAb compact p -adic Lie group vanishes at −2

DOI10.1112/blms/bdt090zbMath1292.22006arXiv1302.5566OpenAlexW2040940467MaRDI QIDQ5409107

Jon González-Sánchez, Andrei Jaikin-Zapirain, Benjamin Klopsch

Publication date: 14 April 2014

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.5566

zbMATH Keywords

profinite group\(p\)-adic Lie grouprepresentation zeta functionFAb group

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Other Dirichlet series and zeta functions (11M41) Representations of Lie and linear algebraic groups over local fields (22E50) Limits, profinite groups (20E18)

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Triple mean values of Witten \(L\)-functions ⋮ Unnamed Item ⋮ Computing local zeta functions of groups, algebras, and modules ⋮ Mean values of the Witten \(L\)-function for \(\mathrm{SU}(2)\) ⋮ Similarity classes of integral p-adic matrices and representation zeta functions of groups of type A₂ ⋮ Zeta functions associated to admissible representations of compact 𝑝-adic Lie groups

Cites Work

• Unnamed Item
• Zeros of Witten zeta functions and absolute limit
• Complex group algebras of finite groups: Brauer's problem 1.
• Zeta functions of groups and rings: Uniformity
• Representation zeta functions of compact \(p\)-adic analytic groups and arithmetic groups
• Completely reducible infinite-dimensional skew linear groups
• Representation growth of linear groups
• Zeros and special values of Witten zeta functions and Witten \(L\)-functions
• Representation zeta functions of some compact 𝑝-adic analytic groups
• Zeta function of representations of compact 𝑝-adic analytic groups

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