On a Continuous Sárközy-Type Problem
Abstract
We prove that there exists a constant ϵ>0ϵ>0 with the following property: if K⊂R2K⊂R2 is a compact set that contains no pair of the form {x,x+(z,z2)}{x,x+(z,z2)} for z≠0z≠0, then dimHK≤2−ϵdimHK≤2−ϵ.
Main Authors
Format
Articles
Research article
Published
2023
Series
Subjects
Publication in research information system
Publisher
Oxford University Press (OUP)
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202211165243Use this for linking
Review status
Peer reviewed
ISSN
1073-7928
DOI
https://doi.org/10.1093/imrn/rnac168
Language
English
Published in
International Mathematics Research Notices
Citation
- Kuca, B., Orponen, T., & Sahlsten, T. (2023). On a Continuous Sárközy-Type Problem. International Mathematics Research Notices, 2023(13), 11291-11315. https://doi.org/10.1093/imrn/rnac168
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Additional information about funding
This work was supported by the Academy of Finland via the projects Quantitative Rectifiability in Euclidean and Non-Euclidean Spaces and Incidences on Fractals [309365, 314172, and 321896 [to B.K. and T.O.]; and by a start-up grant from the University of Manchester [to T.S.].
Copyright© The Author(s) 2022. Published by Oxford University Press. All rights reserved.