Wilkie's conjecture for Pfaffian structures | 数学年鉴

IF 8.3 2区材料科学 Q1 MATERIALS SCIENCE, MULTIDISCIPLINARY

ACS Applied Materials & Interfaces 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

ACS Applied Materials & Interfaces 工程技术-材料科学：综合

CiteScore

16.00

自引率

6.30%

发文量

4978

审稿时长

1.8 months

期刊介绍： ACS Applied Materials & Interfaces is a leading interdisciplinary journal that brings together chemists, engineers, physicists, and biologists to explore the development and utilization of newly-discovered materials and interfacial processes for specific applications. Our journal has experienced remarkable growth since its establishment in 2009, both in terms of the number of articles published and the impact of the research showcased. We are proud to foster a truly global community, with the majority of published articles originating from outside the United States, reflecting the rapid growth of applied research worldwide.