On the Pila–Wilkie theorem

Neer Bhardwaj; Lou van den Dries

doi:10.1016/j.exmath.2022.03.001

On the Pila–Wilkie theorem

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Journal	Expositiones Mathematicae
DOIs	https://doi.org/10.1016/j.exmath.2022.03.001
State	Accepted/In press - 2022

Keywords

Counting theorem
O-minimality

ASJC Scopus subject areas

Mathematics(all)

Online availability

10.1016/j.exmath.2022.03.001

Cite this

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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.",

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AU - Bhardwaj, Neer

AU - van den Dries, Lou

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AB - 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.

KW - Counting theorem

KW - O-minimality

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SN - 0723-0869

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On the Pila–Wilkie theorem

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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