On a Continuous Sárközy-Type Problem-Reference-Cited by-同舟云学术

On a Continuous Sárközy-Type Problem

Published:2022-06-09 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Kuca Borys¹,Orponen Tuomas¹,Sahlsten Tuomas²

Affiliation:

1. Department of Mathematics and Statistics , University of Jyväskylä, P.O. Box 35 (MaD), FI-40014 Jyväskylä, Finland

2. Department of Mathematics and Systems Analysis , Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland

Abstract

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 $.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnac168/44047168/rnac168.pdf

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