On a continuous Sárközy type problem

Borys Kuca; Tuomas Orponen; Tuomas Sahlsten

doi:10.1093/imrn/rnac168

On a continuous Sárközy type problem

Borys Kuca, Tuomas Orponen, Tuomas Sahlsten

Department of Mathematics and Systems Analysis

Research output: Contribution to journal › Article › Scientific › peer-review

Abstract

We prove that there exists a constant ϵ>0 with the following property: if K⊂R2 is a compact set that contains no pair of the form {x,x+(z,z2)} for z≠0⁠, then dimH K≤2−ϵ⁠.

Original language	English
Article number	rnac168
Number of pages	18
Journal	INTERNATIONAL MATHEMATICS RESEARCH NOTICES
Early online date	9 Jun 2022
DOIs	https://doi.org/10.1093/imrn/rnac168
Publication status	E-pub ahead of print - 9 Jun 2022
MoE publication type	A1 Journal article-refereed

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10.1093/imrn/rnac168

https://arxiv.org/abs/2110.15065

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abstract = "We prove that there exists a constant ϵ>0 with the following property: if K⊂R2 is a compact set that contains no pair of the form {x,x+(z,z2)} for z≠0⁠, then dimH K≤2−ϵ⁠.",

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On a continuous Sárközy type problem

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