Wilkie's conjecture for restricted elementary functions

DOI10.4007/annals.2017.186.1.6zbMath1383.11090arXiv1605.04671OpenAlexW2962711163WikidataQ122976121 ScholiaQ122976121MaRDI QIDQ2364597

Gal Binyamini, Dmitri Novikov

Publication date: 21 July 2017

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.04671

zbMATH Keywords

rational pointsmetric entropyPfaffian functionsdefinable sets

Mathematics Subject Classification ID

Arithmetic algebraic geometry (Diophantine geometry) (11G99) Model theory (number-theoretic aspects) (11U09) Model theory of ordered structures; o-minimality (03C64)

Related Items (16)

Rational values of transcendental functions and arithmetic dynamics ⋮ Point counting and Wilkie's conjecture for non-Archimedean Pfaffian and Noetherian functions ⋮ Doubling chains on complements of algebraic hypersurfaces ⋮ On the Pila-Wilkie theorem ⋮ Tameness in geometry and arithmetic: beyond o-minimality ⋮ The Pila–Wilkie theorem for subanalytic families: a complex analytic approach ⋮ Wilkie's conjecture for Pfaffian structures ⋮ Zeroes and rational points of analytic functions ⋮ Pfaffian definitions of Weierstrass elliptic functions ⋮ Density of algebraic points on Noetherian varieties ⋮ Effective Pila-Wilkie bounds for unrestricted Pfaffian surfaces ⋮ Ill-distributed sets over global fields and exceptional sets in diophantine geometry ⋮ Point counting for foliations over number fields ⋮ Complex cellular structures ⋮ Counting rational points and lower bounds for Galois orbits ⋮ Piecewise Weierstrass preparation and division for o-minimal holomorphic functions

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