Uniform rationality of the Poincaré series of definable, analytic equivalence relations on local fields

DOI10.1090/btran/23zbMath1469.11478arXiv1610.07952OpenAlexW2982056368MaRDI QIDQ5240815

Nguyen Huu Kien

Publication date: 29 October 2019

Published in: Transactions of the American Mathematical Society, Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.07952

zbMATH Keywords

motivic integrationanalytic structurenon-Archimedean geometrysubanalytic setszeta functions of groupsrationality of Poincaré seriesdefinable equivalence relationsconstructible motivic functionsuniform \(p\)-adic integration

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Subgroup theorems; subgroup growth (20E07) Model-theoretic algebra (03C60) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Other Dirichlet series and zeta functions (11M41) Model theory (number-theoretic aspects) (11U09) Applications of model theory (03C98) Quantifier elimination, model completeness, and related topics (03C10)

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