Rationality of p-adic Poincaré series: Uniformity in p

DOI10.1016/0168-0072(90)90050-CzbMath0731.12015MaRDI QIDQ807686

Angus J. Macintyre

Publication date: 1990

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

zbMATH Keywords

rationalityp-adic Poincaré seriesquantifier-elimination

Mathematics Subject Classification ID

Local ground fields in algebraic geometry (14G20) Applications of logic to commutative algebra (13L05) Model theory of fields (12L12) Quantifier elimination, model completeness, and related topics (03C10)

Related Items (13)

Zeta functions of groups and rings: Uniformity ⋮ Between the Rings $${\mathbb Z}/p^n{\mathbb Z}$$ and the Ring $${\mathbb Z}_p$$: Issues of Axiomatizability, Definability and Decidability ⋮ Ideal growth in amalgamated powers of nilpotent rings of class two and zeta functions of quiver representations ⋮ Definable sets, motives and 𝑝-adic integrals ⋮ On the idea(l) of logical closure ⋮ Uniform properties of rigid subanalytic sets ⋮ REDUCTIONS OF POINTS ON ALGEBRAIC GROUPS ⋮ Arithmetic lattices in unipotent algebraic groups ⋮ Zeta functions related to the group of \(\text{SL}_2(\mathbb{Z}_p)\) ⋮ Uniform rationality of the Poincaré series of definable, analytic equivalence relations on local fields ⋮ Analytic cell decomposition and analytic motivic integration ⋮ On singularity properties of convolutions of algebraic morphisms ‐ the general case ⋮ Pro-isomorphic zeta functions of nilpotent groups and Lie rings under base extension

Cites Work

• The rationality of the Poincaré series associated to the p-adic points on a variety
• Subgroups of finite index in nilpotent groups
• Model theoretic algebra. Selected topics
• The elementary theory of finite fields
• On the structure of semialgebraic sets over p-adic fields
• p-adic semi-algebraic sets and cell decomposition.
• Algebraic theories with definable Skolem functions
• Uniform p-adic cell decomposition and local zeta functions.
• On definable subsets of p-adic fields
• Bounds on transfer principles for algebraically closed and complete discretely valued fields
• Decision procedures for real and p‐adic fields
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