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dc.contributor.authorOrponen, Tuomas
dc.date.accessioned2024-06-20T08:42:25Z
dc.date.available2024-06-20T08:42:25Z
dc.date.issued2024
dc.identifier.citationOrponen, T. (2024). On the discretised ABC sum-product problem. <i>Transactions of the American Mathematical Society</i>, <i>Early online</i>. <a href="https://doi.org/10.1090/tran/9094" target="_blank">https://doi.org/10.1090/tran/9094</a>
dc.identifier.otherCONVID_220759217
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/96064
dc.description.abstractLet 0 < beta <= alpha < 1 and kappa > 0. I prove that there exists eta > 0 such that the following holds for every pair of Borel sets A, B subset of R with dim(H) A = alpha and dim(H) B = beta: dim(H) {c is an element of R : dim(H) (A + cB) <= alpha + eta} <= alpha-beta/1-beta + kappa. This extends a result of Bourgain from 2010, which contained the case alpha = beta. The paper also contains a delta-discretised, and somewhat stronger, version of the estimate above, and new information on the size of long sums of the form alpha B-1 + ... + alpha B-n..en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherAmerican Mathematical Society
dc.relation.ispartofseriesTransactions of the American Mathematical Society
dc.rightsCC BY-NC 4.0
dc.subject.otherdiscretised sum-product problem
dc.subject.otherprojections
dc.subject.otherHausdorff dimension.
dc.titleOn the discretised ABC sum-product problem
dc.typeresearch article
dc.identifier.urnURN:NBN:fi:jyu-202406204828
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.relation.issn0002-9947
dc.relation.volumeEarly online
dc.type.versionacceptedVersion
dc.rights.copyright© 2023 the Authors
dc.rights.accesslevelopenAccessfi
dc.type.publicationarticle
dc.relation.grantnumber335479
dc.relation.grantnumber343530
dc.relation.grantnumber343256
dc.subject.ysokombinatoriikka
dc.subject.ysofraktaalit
dc.subject.ysolukuteoria
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p4745
jyx.subject.urihttp://www.yso.fi/onto/yso/p6341
jyx.subject.urihttp://www.yso.fi/onto/yso/p1988
dc.rights.urlhttps://creativecommons.org/licenses/by-nc/4.0/
dc.relation.doi10.1090/tran/9094
dc.relation.funderResearch Council of Finlanden
dc.relation.funderResearch Council of Finlanden
dc.relation.funderResearch Council of Finlanden
dc.relation.funderSuomen Akatemiafi
dc.relation.funderSuomen Akatemiafi
dc.relation.funderSuomen Akatemiafi
jyx.fundingprogramResearch costs of Academy Research Fellow, AoFen
jyx.fundingprogramAcademy Project, AoFen
jyx.fundingprogramAcademy Research Fellow, AoFen
jyx.fundingprogramAkatemiatutkijan tutkimuskulut, SAfi
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundingprogramAkatemiatutkija, SAfi
jyx.fundinginformationThe author was supported by the Academy of Finland via the projects Quantitative rectifiability in Euclidean and non-Euclidean spaces and Incidences on Fractals, grant Nos. 309365, 314172, 321896.
dc.type.okmA1


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