Normal zeta functions of the Heisenberg groups over number rings. II: The non-split case.

DOI10.1007/s11856-015-1271-8zbMath1343.20031arXiv1401.0266OpenAlexW1532101635MaRDI QIDQ273085

Christopher Voll, Michael M. Schein

Publication date: 21 April 2016

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.0266

zbMATH Keywords

subgroups of finite indexfunctional equationsHeisenberg groupsnormal zeta functionsrings of integers of number fields

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Factorials, binomial coefficients, combinatorial functions (05A10) Subgroup theorems; subgroup growth (20E07) Nilpotent groups (20F18) Other Dirichlet series and zeta functions (11M41) Linear algebraic groups over global fields and their integers (20G30)

Related Items (11)

Zeta functions of the 3-dimensional almost-Bieberbach groups ⋮ Ideal growth in amalgamated powers of nilpotent rings of class two and zeta functions of quiver representations ⋮ Generalized Igusa functions and ideal growth in nilpotent Lie rings ⋮ The cotype zeta function of \(\mathbb{Z}^d\) ⋮ Normal zeta functions of the Heisenberg groups over number rings I: the unramified case ⋮ Generalized Igusa functions and ideal growth in nilpotent Lie rings ⋮ Zeta functions of groups and rings -- functional equations and analytic uniformity ⋮ Zeta functions enumerating normal subgroups of \(\mathfrak{T}_2\)-groups and their behavior on residue classes ⋮ On the degree of polynomial subgroup growth of nilpotent groups ⋮ Pro-isomorphic zeta functions of nilpotent groups and Lie rings under base extension ⋮ Uniform analytic properties of representation zeta functions of finitely generated nilpotent groups

Cites Work

• Functional equations for zeta functions of groups and rings
• Subgroups of finite index in nilpotent groups
• Zeta functions of groups and rings
• Functional equations for local normal zeta functions of nilpotent groups. With an appendix by A. Beauville.
• Normal zeta functions of the Heisenberg groups over number rings I: the unramified case
• Igusa-type functions associated to finite formed spaces and their functional equations
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