Zeta functions of groups and rings: Uniformity

DOI10.1007/BF02773672zbMath0865.20021OpenAlexW2000606791MaRDI QIDQ1327498

Marcus P. F. du Sautoy

Publication date: 12 July 1994

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

Full work available at URL: https://doi.org/10.1007/bf02773672

zbMATH Keywords

subgroups of finite indexEuler productszeta functionsprofinite completionsprofinite groupstorsion-free nilpotent groups\(p\)-adic analytic groups\(p\)-adic integrals

Mathematics Subject Classification ID

Nilpotent groups (20F18) Other Dirichlet series and zeta functions (11M41) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Analysis on (p)-adic Lie groups (22E35) Zeta functions and (L)-functions (11S40) Limits, profinite groups (20E18) Quantifier elimination, model completeness, and related topics (03C10) Non-Archimedean analysis (32P05)

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The representation zeta function of a FAb compact p -adic Lie group vanishes at −2 ⋮ Natural boundaries of Dirichlet series ⋮ Integrating on \(p\)-adic Lie groups ⋮ Zeta functions related to the group of \(\text{SL}_2(\mathbb{Z}_p)\) ⋮ Counting finite index subrings of $\mathbb Z^n$ ⋮ Pro-isomorphic zeta functions of nilpotent groups and Lie rings under base extension

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