Simultaneous Diophantine approximation on the three dimensional Veronese curve
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908470628843520 |
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| author | Badziahin, Dmitry |
| author_facet | Badziahin, Dmitry |
| contents | We compute the Hausdorff dimension of the set of simultaneously $λ$-well approximable points on the Veronese curve in $\RR^3$ for $1/3\le λ\le 3/5$. This range for $λ$ was predicted in the conjecture of Beresnevich and Yang from~\cite{ber_yan_2023}. To the best of the author's knowledge, this makes $\VVV_3$ the first nondegenerate curve in $\RR^n$, $n\ge 3$, to confirm the lower bound part of this conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21401 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simultaneous Diophantine approximation on the three dimensional Veronese curve Badziahin, Dmitry Number Theory 11J13, 11J54, 11J82, 11K55 We compute the Hausdorff dimension of the set of simultaneously $λ$-well approximable points on the Veronese curve in $\RR^3$ for $1/3\le λ\le 3/5$. This range for $λ$ was predicted in the conjecture of Beresnevich and Yang from~\cite{ber_yan_2023}. To the best of the author's knowledge, this makes $\VVV_3$ the first nondegenerate curve in $\RR^n$, $n\ge 3$, to confirm the lower bound part of this conjecture. |
| title | Simultaneous Diophantine approximation on the three dimensional Veronese curve |
| topic | Number Theory 11J13, 11J54, 11J82, 11K55 |
| url | https://arxiv.org/abs/2507.21401 |