English

On the Pila-Wilkie theorem

Logic 2022-09-12 v3 Algebraic Geometry Number Theory

Abstract

This expository paper gives 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 also include complete treatments of a result due to Pila and Bombieri and of the o-minimal Yomdin-Gromov theorem that are used in this proof. For the latter we follow Binyamini and Novikov.

Keywords

Cite

@article{arxiv.2010.14046,
  title  = {On the Pila-Wilkie theorem},
  author = {Neer Bhardwaj and Lou van den Dries},
  journal= {arXiv preprint arXiv:2010.14046},
  year   = {2022}
}

Comments

43 pages

R2 v1 2026-06-23T19:40:27.983Z