On the Exact Fourier Dimension of Sets of Well-Approximable Matrices
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913288557690880 |
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| author | Cai, Thomas Hambrook, Kyle |
| author_facet | Cai, Thomas Hambrook, Kyle |
| contents | We compute the exact Fourier dimension of the set of $Ψ$-well-approximable $m \times n$ matrices (and the set of $Ψ$-well-approximable numbers) in the homogeneous and inhomogeneous cases for any approximation function $Ψ$ satisfying $\sum_{q \in \mathbb{Z}^n} Ψ(q)^m < \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19410 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Exact Fourier Dimension of Sets of Well-Approximable Matrices Cai, Thomas Hambrook, Kyle Number Theory We compute the exact Fourier dimension of the set of $Ψ$-well-approximable $m \times n$ matrices (and the set of $Ψ$-well-approximable numbers) in the homogeneous and inhomogeneous cases for any approximation function $Ψ$ satisfying $\sum_{q \in \mathbb{Z}^n} Ψ(q)^m < \infty$. |
| title | On the Exact Fourier Dimension of Sets of Well-Approximable Matrices |
| topic | Number Theory |
| url | https://arxiv.org/abs/2403.19410 |