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

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arxiv 2403.19410 v1 pith:D47A6VMX submitted 2024-03-28 math.NT

classification math.NT
keywords well-approximabledimensionexactfouriermatricesapproximationcasescompute
verification ladder T0 review T1 audit T2 compute T3 formal
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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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