An upper bound of the Hausdorff dimension of singular vectors on affine subspaces
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916470549643264 |
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| author | Shah, Nimish A. Yang, Pengyu |
| author_facet | Shah, Nimish A. Yang, Pengyu |
| contents | In Diophantine approximation, the notion of singular vectors was introduced by Khintchine in the 1920's. We study the set of singular vectors on an affine subspace of $\mathbb{R}^n$. We give an upper bound of its Hausdorff dimension in terms of the Diophantine exponent of the parameter of the affine subspace. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05834 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An upper bound of the Hausdorff dimension of singular vectors on affine subspaces Shah, Nimish A. Yang, Pengyu Number Theory Dynamical Systems 37A17, 11J83, 22E46 In Diophantine approximation, the notion of singular vectors was introduced by Khintchine in the 1920's. We study the set of singular vectors on an affine subspace of $\mathbb{R}^n$. We give an upper bound of its Hausdorff dimension in terms of the Diophantine exponent of the parameter of the affine subspace. |
| title | An upper bound of the Hausdorff dimension of singular vectors on affine subspaces |
| topic | Number Theory Dynamical Systems 37A17, 11J83, 22E46 |
| url | https://arxiv.org/abs/2311.05834 |