The Pila–Wilkie theorem for subanalytic families: a complex analytic approach

DOI10.1112/S0010437X17007333zbMath1427.11052arXiv1605.04537OpenAlexW2401954616MaRDI QIDQ5360289

Gal Binyamini, Dmitri Novikov

Publication date: 28 September 2017

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.04537

zbMATH Keywords

rational pointsdefinable setsinterpolation determinantsBombieri-Pila theorem

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Real-analytic and semi-analytic sets (14P15) Semi-analytic sets, subanalytic sets, and generalizations (32B20) Model theory (number-theoretic aspects) (11U09) Model theory of ordered structures; o-minimality (03C64) Analytic algebras and generalizations, preparation theorems (32B05)

Related Items (8)

Wilkie's conjecture for restricted elementary functions ⋮ Point counting and Wilkie's conjecture for non-Archimedean Pfaffian and Noetherian functions ⋮ Doubling chains on complements of algebraic hypersurfaces ⋮ Zeroes and rational points of analytic functions ⋮ Density of algebraic points on Noetherian varieties ⋮ Point counting for foliations over number fields ⋮ Complex cellular structures ⋮ Piecewise Weierstrass preparation and division for o-minimal holomorphic functions

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