Zeta functions of groups and rings – recent developments

DOI10.1017/CBO9781316227343.031zbMath1377.11103arXiv1409.7955MaRDI QIDQ2990062

Christopher Voll

Publication date: 29 July 2016

Published in: Groups St Andrews 2013 (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.7955

zbMATH Keywords

\(p\)-adic integrationDirichlet serieszeta functionsfinitely generated nilpotent groupsarithmetic groupsrepresentation growthKirillov orbit methodIgusa-type zeta functionssubgroup and subring growth

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Subgroup theorems; subgroup growth (20E07) Nilpotent groups (20F18) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Other Dirichlet series and zeta functions (11M41) Linear algebraic groups over global fields and their integers (20G30) Asymptotic properties of groups (20F69) Linear algebraic groups over local fields and their integers (20G25) Research exposition (monographs, survey articles) pertaining to group theory (20-02)

Related Items (11)

Zeta functions of the 3-dimensional almost-Bieberbach groups ⋮ Stability results for local zeta functions of groups algebras, and modules ⋮ A Framework for Computing Zeta Functions of Groups, Algebras, and Modules ⋮ Enumerating submodules invariant under an endomorphism ⋮ Similarity classes of integral p-adic matrices and representation zeta functions of groups of type A₂ ⋮ Generalized zeta function representation of groups and 2-dimensional topological Yang-Mills theory: The example of GL(2, 𝔽q) and PGL(2, 𝔽q) ⋮ Zeta functions of groups and rings -- functional equations and analytic uniformity ⋮ Zeta functions associated to admissible representations of compact 𝑝-adic Lie groups ⋮ Counting finite index subrings of $\mathbb Z^n$ ⋮ On the degree of polynomial subgroup growth of nilpotent groups ⋮ Uniform analytic properties of representation zeta functions of finitely generated nilpotent groups

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