On a Continuous Sárközy-Type Problem

Kuca, Borys; Orponen, Tuomas; Sahlsten, Tuomas

doi:10.1093/imrn/rnac168

dc.contributor.author	Kuca, Borys
dc.contributor.author	Orponen, Tuomas
dc.contributor.author	Sahlsten, Tuomas
dc.date.accessioned	2022-11-16T12:28:37Z
dc.date.available	2022-11-16T12:28:37Z
dc.date.issued	2023
dc.identifier.citation	Kuca, B., Orponen, T., & Sahlsten, T. (2023). On a Continuous Sárközy-Type Problem. <i>International Mathematics Research Notices</i>, <i>2023</i>(13), 11291-11315. <a href="https://doi.org/10.1093/imrn/rnac168" target="_blank">https://doi.org/10.1093/imrn/rnac168</a>
dc.identifier.other	CONVID_147103381
dc.identifier.uri	https://jyx.jyu.fi/handle/123456789/83949
dc.description.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−ϵdimH⁡K≤2−ϵ⁠.	en
dc.format.mimetype	application/pdf
dc.language.iso	eng
dc.publisher	Oxford University Press (OUP)
dc.relation.ispartofseries	International Mathematics Research Notices
dc.rights	In Copyright
dc.subject.other	fractals
dc.subject.other	polynomial configurations
dc.subject.other	Hausdorff dimension
dc.subject.other	Fourier transforms of measures
dc.subject.other	Szemerédi’s theorem
dc.subject.other	minimeasures
dc.subject.other	finite fields
dc.title	On a Continuous Sárközy-Type Problem
dc.type	article
dc.identifier.urn	URN:NBN:fi:jyu-202211165243
dc.contributor.laitos	Matematiikan ja tilastotieteen laitos	fi
dc.contributor.laitos	Department of Mathematics and Statistics	en
dc.type.uri	http://purl.org/eprint/type/JournalArticle
dc.type.coar	http://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatus	peerReviewed
dc.format.pagerange	11291-11315
dc.relation.issn	1073-7928
dc.relation.numberinseries	13
dc.relation.volume	2023
dc.type.version	acceptedVersion
dc.rights.copyright	© The Author(s) 2022. Published by Oxford University Press. All rights reserved.
dc.rights.accesslevel	openAccess	fi
dc.subject.yso	polynomit
dc.subject.yso	harmoninen analyysi
dc.subject.yso	fraktaalit
dc.subject.yso	mittateoria
dc.format.content	fulltext
jyx.subject.uri	http://www.yso.fi/onto/yso/p17241
jyx.subject.uri	http://www.yso.fi/onto/yso/p28124
jyx.subject.uri	http://www.yso.fi/onto/yso/p6341
jyx.subject.uri	http://www.yso.fi/onto/yso/p13386
dc.rights.url	http://rightsstatements.org/page/InC/1.0/?language=en
dc.relation.doi	10.1093/imrn/rnac168
jyx.fundinginformation	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.].
dc.type.okm	A1