Submission date: 27 October 2020

Abstract:

In this expository paper we give an account of the Pila-Wilkie counting theorem and some of its extensions and generalizations. We use semialgebraic cell decomposition to simplify part of the original proof. We include a full treatment of a result due to Pila and Bombieri, and of a variant of the Yomdin-Gromov theorem that are used in this proof.

Mathematics Subject Classification: 03C64 (Primary) 11G99 (Secondary)

Keywords and phrases:

Full text arXiv 2010.14046: pdf, ps.