A Remark on the Set of Exactly Approximable Vectors in the Simultaneous Case
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916095719374848 |
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| author | Fregoli, Reynold |
| author_facet | Fregoli, Reynold |
| contents | We compute the Hausdorff dimension of the set of $ψ$-exactly approximable vectors, in the simultaneous case, in dimension strictly larger than $2$ and for approximating functions $ψ$ 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 Jarník's Theorem on fibres. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01730 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Remark on the Set of Exactly Approximable Vectors in the Simultaneous Case Fregoli, Reynold Number Theory 11J13, 11J83 We compute the Hausdorff dimension of the set of $ψ$-exactly approximable vectors, in the simultaneous case, in dimension strictly larger than $2$ and for approximating functions $ψ$ 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 Jarník's Theorem on fibres. |
| title | A Remark on the Set of Exactly Approximable Vectors in the Simultaneous Case |
| topic | Number Theory 11J13, 11J83 |
| url | https://arxiv.org/abs/2304.01730 |