Wilkie's conjecture for restricted elementary functions

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Grenoble
[MATH]Mathematics [math]
Foliations and algebraic geometry
eem2019
Feuilletages et géométrie algébrique
restricted elementary functions
Wilkie's conjecture

Appears in collection : Summer School 2019 - Foliations and algebraic geometry

We consider the structure $\mathbb{R}^{RE}$ obtained from $(\mathbb{R},<,+,⋅)$ by adjoining the restricted exponential and sine functions. We prove Wilkie's conjecture for sets definable in this structure: the number of rational points of height $H$ in the transcendental part of any definable set is bounded by a polynomial in $\log H$.