6533b860fe1ef96bd12c39e9
RESEARCH PRODUCT
On a Continuous Sárközy-Type Problem
Borys KucaTuomas OrponenTuomas Sahlstensubject
Szemerédi’s theoremfractalsGeneral Mathematicspolynomitpolynomial configurationsHausdorff dimensionfraktaalitmittateoriafinite fieldsharmoninen analyysiFourier transforms of measuresminimeasuresdescription
Abstract 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 $.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2022-06-09 | International Mathematics Research Notices |