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

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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