On a continuous Sárközy type problem
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866914711895801856 |
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| author | Kuca, Borys Orponen, Tuomas Sahlsten, Tuomas |
| author_facet | Kuca, Borys Orponen, Tuomas Sahlsten, Tuomas |
| contents | We prove that there exists a constant $\varepsilon > 0$ with the following property: if $K \subset \mathbb{R}^{2}$ is a compact set which contains no pair of the form $\{x, x + (z, z^{2})\}$ for $z \neq 0$, then $\mathrm{dim}_\mathrm{H} K \leq 2 - \varepsilon$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2110_15065 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On a continuous Sárközy type problem Kuca, Borys Orponen, Tuomas Sahlsten, Tuomas Classical Analysis and ODEs Combinatorics Metric Geometry Number Theory 28A80 (primary), 42A38, 11B25, 11B30 (secondary) We prove that there exists a constant $\varepsilon > 0$ with the following property: if $K \subset \mathbb{R}^{2}$ is a compact set which contains no pair of the form $\{x, x + (z, z^{2})\}$ for $z \neq 0$, then $\mathrm{dim}_\mathrm{H} K \leq 2 - \varepsilon$. |
| title | On a continuous Sárközy type problem |
| topic | Classical Analysis and ODEs Combinatorics Metric Geometry Number Theory 28A80 (primary), 42A38, 11B25, 11B30 (secondary) |
| url | https://arxiv.org/abs/2110.15065 |