A remark on the set of exactly approximable vectors in the simultaneous case

IF 0.8 3区数学 Q2 MATHEMATICS Proceedings of the American Mathematical Society Pub Date : 2024-06-14 DOI:10.1090/proc/16790

Reynold Fregoli

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引用次数: 1

Abstract

We compute the Hausdorff dimension of the set of ψ \psi -exactly approximable vectors, in the simultaneous case, in dimension strictly larger than 2 2 and for approximating functions ψ \psi with order at infinity less than or equal to − 2 -2 . Our method relies on the analogous result in dimension 1 1 , proved by Yann Bugeaud and Carlos Moreira, and a version of Jarník’s theorem on fibres.

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关于同时情况下精确可近似向量集的评论

我们计算了ψ \psi精确可近似向量集的豪斯多夫维度，在同时情况下，维度严格大于2 2，且近似函数ψ \psi在无穷远处的阶小于或等于- 2 -2。我们的方法依赖于扬-布热奥（Yann Bugeaud）和卡洛斯-莫雷拉（Carlos Moreira）在维度 1 1 中证明的类似结果，以及雅尼克（Jarník）关于纤维的定理版本。

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.