Effective Pila--Wilkie bounds for unrestricted Pfaffian surfaces

Gareth Jones; Margaret Thomas

doi:10.1007/s00208-020-02029-x

Effective Pila--Wilkie bounds for unrestricted Pfaffian surfaces

Gareth Jones, Margaret Thomas

Pure Mathematics

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Abstract

We prove effective Pila--Wilkie estimates for the number of rational points of bounded height lying on certain surfaces defined by Pfaan
functions. The class of surfaces to which our result applies includes, for instance, graphs of unrestricted Pfaan functions defined on the plane.

Original language	English
Pages (from-to)	0
Journal	Mathematische Annalen
Volume	0
DOIs	https://doi.org/10.1007/s00208-020-02029-x
Publication status	Published - 25 Jul 2020

Keywords

Pfaffian functions
effectivity
rational points
the Pila--Wilkie Theorem

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EffectivePWunrestrictedPfaffiansurfaces6Accepted author manuscript, 476 KB

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abstract = "We prove effective Pila--Wilkie estimates for the number of rational points of bounded height lying on certain surfaces defined by Pfaanfunctions. The class of surfaces to which our result applies includes, for instance, graphs of unrestricted Pfaan functions defined on the plane.",

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KW - Pfaffian functions

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KW - rational points

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Effective Pila--Wilkie bounds for unrestricted Pfaffian surfaces

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Keywords

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