Zeta functions of three-dimensional \(p\)-adic Lie algebras

DOI10.1007/s00209-008-0416-4zbMath1193.11083arXiv0710.1970OpenAlexW2046831764MaRDI QIDQ834791

Christopher Voll, Benjamin Klopsch

Publication date: 27 August 2009

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.1970

zbMATH Keywords

subgroup growthIgusa's local zeta function\(\mathbb Z_p\)-Lie algebrassubalgebra zeta function

Mathematics Subject Classification ID

General ternary and quaternary quadratic forms; forms of more than two variables (11E20) Lie algebras and Lie superalgebras (17B99) Zeta and (L)-functions in characteristic (p) (11M38)

Related Items

Zeta functions of the 3-dimensional almost-Bieberbach groups, A new generating function for calculating the Igusa local zeta function, A Framework for Computing Zeta Functions of Groups, Algebras, and Modules, Igusa-type functions associated to finite formed spaces and their functional equations, Functional equations for zeta functions of groups and rings, The cotype zeta function of \(\mathbb{Z}^d\), Computing local zeta functions of groups, algebras, and modules, Classification of three-dimensional solvable \(p\)-adic Leibniz algebras, Computing topological zeta functions of groups, algebras, and modules, I, On the degree of polynomial subgroup growth of nilpotent groups

Cites Work

• Unnamed Item
• Unnamed Item
• Functional equations for zeta functions of groups and rings
• Subgroups of finite index in nilpotent groups
• Zeta functions related to the group of \(\text{SL}_2(\mathbb{Z}_p)\)
• On the Lie theory of \(p\)-adic analytic groups
• Subgroup growth.
• Zeta functions of groups and rings
• The zeta function of [sfr [lfr ]₂ and resolution of singularities]
• Analytic pro-p groups of small dimensions
• COUNTING SUBGROUPS IN A FAMILY OF NILPOTENT SEMI-DIRECT PRODUCTS
• A Functional Equation of Igusa's Local Zeta Function
• An Invariant on 3-Dimensional Lie Algebras
• Complex powers and asymptotic expansions. II.
• Zeta functions related to the pro- $p$ group SL $_1${\bfseries (}$\Delta_{\hbox{\scriptsize{\bfseries\itshape p}}}${\bfseries )$ }
• Positively finitely generated groups
• The zeta function of sl2(ℤ)
• Analytic properties of zeta functions and subgroup growth