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arXiv · 2403.19410

On the Exact Fourier Dimension of Sets of Well-Approximable Matrices

Thomas Cai·Kyle Hambrook
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Abstract

We compute the exact Fourier dimension of the set of $\Psi$-well-approximable $m \times n$ matrices (and the set of $\Psi$-well-approximable numbers) in the homogeneous and inhomogeneous cases for any approximation function $\Psi$ satisfying $\sum_{q \in \mathbb{Z}^n} \Psi(q)^m < \infty$.

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Thomas Cai, Kyle Hambrook. 2024-03-28. On the Exact Fourier Dimension of Sets of Well-Approximable Matrices. https://arxiv.org/abs/2403.19410

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