On a Continuous Sárközy-Type Problem
نویسندگان
چکیده
Abstract We prove that there exists a constant $\epsilon> 0$ with the following property: if $K \subset {\mathbb {R}}^2$ is compact set contains no pair of form $\{x, x + (z, z^{2})\}$ for $z \neq 0$, then $\dim _{\textrm {H}} K \leq 2 - \epsilon $.
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2022
ISSN: ['1687-0247', '1073-7928']
DOI: https://doi.org/10.1093/imrn/rnac168