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arXiv · 2304.01730

A Remark on the Set of Exactly Approximable Vectors in the Simultaneous Case

Reynold Fregoli
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Abstract

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

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Reynold Fregoli. 2023-04-04. A Remark on the Set of Exactly Approximable Vectors in the Simultaneous Case. https://arxiv.org/abs/2304.01730

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