Wilkie's conjecture for Pfaffian structures | 数学年鉴

IF 5.7 1区数学 Q1 MATHEMATICS

Annals of Mathematics Pub Date : 2024-03-05 DOI:10.4007/annals.2024.199.2.5

Gal Binyamini, Dmitry Novikov, Benny Zak

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引用次数: 0

摘要

我们证明了威尔基猜想在受限子普法非函数生成的结构中的有效形式：高度为 $H$ 的有理点的数目位于这样一个集合的超越部分，其增长速度不超过 $\log H$ 的某个幂。我们的界限只取决于相关集合的普法因子复杂性。作为推论，我们推导出威尔基对 $\mathbb{R}_{\rm exp}$ 的最初猜想的全部一般性。

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Wilkie’s conjecture for Pfaffian structures | Annals of Mathematics

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 $\log H$. Our bounds depend only on the Pfaffian complexity of the sets involved. As a corollary we deduce Wilkie’s original conjecture for $\mathbb{R}_{\rm exp}$ in full generality.

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来源期刊

Annals of Mathematics 数学-数学

CiteScore

9.10

自引率

2.00%

发文量

审稿时长

12 months

期刊介绍： The Annals of Mathematics is published bimonthly by the Department of Mathematics at Princeton University with the cooperation of the Institute for Advanced Study. Founded in 1884 by Ormond Stone of the University of Virginia, the journal was transferred in 1899 to Harvard University, and in 1911 to Princeton University. Since 1933, the Annals has been edited jointly by Princeton University and the Institute for Advanced Study.