Geodesic
Wilkie’s conjecture for restricted elementary functions
Gal Binyamini1 ; Dmitry Novikov1
1 Weizmann Institute of Science, Rehovot, Israel
Annals of mathematics, Tome 186 (2017) no. 1, pp. 237-275.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We consider the structure $\mathbb{R}^{\mathrm{RE}}$ obtained from $(\mathbb{R},<,+,\cdot)$ 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 $\log H$. We also prove two refined conjectures due to Pila concerning the density of algebraic points from a fixed number field, or with a fixed algebraic degree, for $\mathbb{R}^{\mathrm{RE}}$-definable sets.
DOI : 10.4007/annals.2017.186.1.6

Gal Binyamini 1 ; Dmitry Novikov 1

1 Weizmann Institute of Science, Rehovot, Israel 
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Gal Binyamini; Dmitry Novikov. Wilkie’s conjecture for restricted elementary functions. Annals of mathematics, Tome 186 (2017) no. 1, pp. 237-275. doi : 10.4007/annals.2017.186.1.6. http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.186.1.6/

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