曲线上严重逼近点的致胜性质

IF 2.3 1区数学 Q1 MATHEMATICS

Duke Mathematical Journal Pub Date : 2020-05-05 DOI:10.1215/00127094-2022-0038

V. Beresnevich, Erez Nesharim, Lei Yang

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引用次数: 6

摘要

本文证明了$\mathbb{R}^n$中任意解析非退化曲线上的差逼近点是一个绝对胜利集。这证实了Badziahin和Velani(2014)在该领域提出的一个关键猜想，该猜想代表了对20世纪60年代达文波特问题的深远概括。在我们的主要结果的各种结果中，有一个关于实数的Bugeaud问题的解，它被任意次的代数数严重逼近。

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Winning property of badly approximable points on curves

In this paper we prove that badly approximable points on any analytic non-degenerate curve in $\mathbb{R}^n$ is an absolute winning set. This confirms a key conjecture in the area stated by Badziahin and Velani (2014) which represents a far-reaching generalisation of Davenport's problem from the 1960s. Amongst various consequences of our main result is a solution to Bugeaud's problem on real numbers badly approximable by algebraic numbers of arbitrary degree.

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