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

University of Jyväskylä

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

3 Citations (Scopus)

Abstract

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

Original language	English
Article number	rnac168
Pages (from-to)	11291–11315
Number of pages	25
Journal	International Mathematics Research Notices
Volume	2023
Issue number	13
Early online date	9 Jun 2022
DOIs	https://doi.org/10.1093/imrn/rnac168
Publication status	Published - 1 Jun 2023
MoE publication type	A1 Journal article-refereed

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10.1093/imrn/rnac168

https://arxiv.org/abs/2110.15065

Cite this

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title = "On a continuous S{\'a}rk{\"o}zy type problem",

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

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

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On a continuous Sárközy type problem

Abstract

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