Abstract
We prove an effective form of Wilkie's conjecture in the structure generated by restricted sub-Pfaffian functions: the number of rational points of height $H$ lying in the transcendental part of such a set grows no faster than some power of $\mathrm{log}\, H$. Our bounds depend only on the Pfaffian complexity of the sets involved. As a corollary we deduce Wilkie's original conjecture for $\mathbb{R}_{\mathrm{exp}}$ in full generality.
Citation
Gal Binyamini. Dmitry Novikov. Benny Zak. "Wilkie's conjecture for Pfaffian structures." Ann. of Math. (2) 199 (2) 795 - 821, March 2024. https://doi.org/10.4007/annals.2024.199.2.5
Information