Computing local zeta functions of groups, algebras, and modules

DOI10.1090/tran/7361zbMath1440.11175arXiv1602.00919OpenAlexW2963637632MaRDI QIDQ4635481

Tobias Rossmann

Publication date: 23 April 2018

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

Full work available at URL: https://arxiv.org/abs/1602.00919

zbMATH Keywords

unipotent groupsLie algebrassubgroup growthzeta functionsrepresentation growth

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Nilpotent groups (20F18) Other Dirichlet series and zeta functions (11M41) Linear algebraic groups over global fields and their integers (20G30) Asymptotic properties of groups (20F69)

Related Items (14)

Zeta functions of the 3-dimensional almost-Bieberbach groups ⋮ A Framework for Computing Zeta Functions of Groups, Algebras, and Modules ⋮ Groups, Graphs, and Hypergraphs: Average Sizes of Kernels of Generic Matrices with Support Constraints ⋮ Linear relations with disjoint supports and average sizes of kernels ⋮ Computing zeta functions of table algebra orders using local zeta integrals ⋮ Generalized Igusa functions and ideal growth in nilpotent Lie rings ⋮ Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes, II: Groups of type F, G, and H ⋮ Generalized Igusa functions and ideal growth in nilpotent Lie rings ⋮ Enumerating graded ideals in graded rings associated to free nilpotent Lie rings ⋮ 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 ⋮ Counting finite index subrings of $\mathbb Z^n$ ⋮ On the degree of polynomial subgroup growth of nilpotent groups

Cites Work

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• Counting irreducible representations of the Heisenberg group over the integers of a quadratic number field.
• Functional equations for zeta functions of groups and rings
• Computing topological zeta functions of groups, algebras, and modules. II.
• Zeta functions of three-dimensional \(p\)-adic Lie algebras
• Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2
• Topological representation zeta functions of unipotent groups
• Integer points in polyhedra
• Subgroups of finite index in nilpotent groups
• Zeta functions and integral representation theory
• Zeta functions related to the group of \(\text{SL}_2(\mathbb{Z}_p)\)
• Motivic zeta functions of infinite-dimensional Lie algebras
• Representation zeta functions of compact \(p\)-adic analytic groups and arithmetic groups
• Graded nilpotent Lie algebras in low dimensions
• Enumerating submodules invariant under an endomorphism
• Zeta functions of groups and rings
• The zeta function of [sfr [lfr ]₂ and resolution of singularities]
• Classification of Solvable Lie Algebras
• Reduced zeta functions of Lie algebras
• Caracteristiques D'Euler-Poincare, Fonctions Zeta Locales et Modifications Analytiques
• Short rational generating functions for lattice point problems
• A Framework for Computing Zeta Functions of Groups, Algebras, and Modules
• A Polynomial Time Algorithm for Counting Integral Points in Polyhedra When the Dimension is Fixed
• Orders of a quartic field
• The zeta function of sl2(ℤ)
• Local Functional Equations for Submodule Zeta Functions Associated to Nilpotent Algebras of Endomorphisms
• Computing topological zeta functions of groups, algebras, and modules, I
• Uniform analytic properties of representation zeta functions of finitely generated nilpotent groups
• The representation zeta function of a FAb compact p -adic Lie group vanishes at −2
• Representation zeta functions of nilpotent groups and generating functions for Weyl groups of type B
• Zeta functions of Lie rings of upper-triangular matrices
• Analytic properties of zeta functions and subgroup growth

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