Uniform analytic properties of representation zeta functions of finitely generated nilpotent groups

DOI10.1090/tran/6879zbMath1475.20059arXiv1503.06947OpenAlexW2962742707MaRDI QIDQ5267974

Christopher Voll, Duong Hoang Dung

Publication date: 14 June 2017

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.06947

zbMATH Keywords

finitely generated nilpotent groupsrepresentation zeta functionsKirillov orbit method\(p\)-adic integrals

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Nilpotent groups (20F18) Other Dirichlet series and zeta functions (11M41) Asymptotic properties of groups (20F69) Representations of Lie and linear algebraic groups over global fields and adèle rings (22E55) Limits, profinite groups (20E18)

Related Items (14)

Enumerating traceless matrices over compact discrete valuation rings ⋮ A Framework for Computing Zeta Functions of Groups, Algebras, and Modules ⋮ Enumerating submodules invariant under an endomorphism ⋮ Groups, Graphs, and Hypergraphs: Average Sizes of Kernels of Generic Matrices with Support Constraints ⋮ Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes, II: Groups of type F, G, and H ⋮ Representation growth of the Heisenberg group over 𝒪[x/(x3)] ⋮ Computing local zeta functions of groups, algebras, and modules ⋮ Representation zeta functions of some nilpotent groups associated to prehomogeneous vector spaces ⋮ Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes. I: Arithmetic properties ⋮ Zeta functions of groups and rings -- functional equations and analytic uniformity ⋮ Zeta functions associated to admissible representations of compact 𝑝-adic Lie groups ⋮ Univariate and bivariate zeta functions of unipotent group schemes of type G ⋮ On the degree of polynomial subgroup growth of nilpotent groups ⋮ Pro-isomorphic zeta functions of nilpotent groups and Lie rings under base extension

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