On a Continuous Sárközy-Type Problem
| Autor: | Borys Kuca, Tuomas Orponen, Tuomas Sahlsten |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | International Mathematics Research Notices. |
| ISSN: | 1687-0247 1073-7928 |
| DOI: | 10.1093/imrn/rnac168 |
| Popis: | We prove that there exists a constant $\epsilon> 0$ with the following property: if $K \subset {\mathbb {R}}^2$ is a compact set that contains no pair of the form $\{x, x + (z, z^{2})\}$ for $z \neq 0$, then $\dim _{\textrm {H}} K \leq 2 - \epsilon $. |
| Databáze: | OpenAIRE |
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