A nilpotent group and its elliptic curve: non-uniformity of local zeta functions of groups

DOI10.1007/BF02784157zbMath0998.20033OpenAlexW2037835676MaRDI QIDQ5957372

Marcus P. F. du Sautoy

Publication date: 3 September 2002

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

Full work available at URL: https://doi.org/10.1007/bf02784157

zbMATH Keywords

elliptic curvessubgroups of finite indexzeta functionsnumbers of subgroupsfinitely generated nilpotent groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Nilpotent groups (20F18) Elliptic curves (14H52) Other Dirichlet series and zeta functions (11M41)

Related Items

The number of conjugacy classes in pattern groups is not a polynomial function, Associating curves of low genus to infinite nilpotent groups via the zeta function., Functional equations for zeta functions of groups and rings, On the degree of polynomial subgroup growth in class 2 nilpotent groups., Natural boundaries for Euler products of Igusa zeta functions of elliptic curves, Ideal growth in amalgamated powers of nilpotent rings of class two and zeta functions of quiver representations, Topological representation zeta functions of unipotent groups, Zeta functions enumerating normal subgroups of \(\mathfrak{T}_2\)-groups and their behavior on residue classes, The normal zeta function of the free class two nilpotent group on four generators., Pro-isomorphic zeta functions of nilpotent groups and Lie rings under base extension

Cites Work

• Subgroups of finite index in nilpotent groups
• Zeta functions and counting finite p-groups
• Analytic properties of Euler products of Igusa-type zeta functions and subgroup growth of nilpotent groups
• Enumerating p -Groups, II: Problems Whose Solution is PORC
• Counting \(p\)-groups and nilpotent groups