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dc.contributor.authorFraser, Jonathan
dc.contributor.authorYu, Han
dc.date.accessioned2022-10-13T23:40:22Z
dc.date.available2022-10-13T23:40:22Z
dc.date.issued2021
dc.identifier269404999
dc.identifier5d2dcc8a-3fdc-439f-a0aa-756cc5876ddc
dc.identifier000731613000009
dc.identifier85120806327
dc.identifier.citationFraser , J & Yu , H 2021 , ' Approximate arithmetic structure in large sets of integers ' , Real Analysis Exchange , vol. 46 , no. 1 , pp. 163-174 . https://doi.org/10.14321/realanalexch.46.1.0163en
dc.identifier.issn0147-1937
dc.identifier.otherORCID: /0000-0002-8066-9120/work/102330469
dc.identifier.urihttps://hdl.handle.net/10023/26191
dc.descriptionFunding: JMF acknowledges financial support from an EPSRC Standard Grant (EP/R015104/1) and a Leverhulme Trust Research Project Grant (RPG-2019-034). HY was financially supported by the University of St Andrews and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No.803711).en
dc.description.abstractWe prove that if a set is `large' in the sense of Erdős, then it approximates arbitrarily long arithmetic progressions in a strong quantitative sense. More specifically, expressing the error in the approximation in terms of the gap length Δ of the progression, we improve a previous result of o(Δ) to O(Δα) for any α∈(0,1).
dc.format.extent2648508
dc.language.isoeng
dc.relation.ispartofReal Analysis Exchangeen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleApproximate arithmetic structure in large sets of integersen
dc.typeJournal articleen
dc.contributor.sponsorEPSRCen
dc.contributor.sponsorThe Leverhulme Trusten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.14321/realanalexch.46.1.0163
dc.description.statusPeer revieweden
dc.date.embargoedUntil2022-10-14
dc.identifier.urlhttps://www.jstor.org/journal/realanalexchen
dc.identifier.urlhttps://projecteuclid.org/journals/real-analysis-exchange/issuesen
dc.identifier.urlhttps://projecteuclid.org/journals/real-analysis-exchange/volume-46/issue-1/Approximate-arithmetic-structure-in-large-sets-of-integers/10.14321/realanalexch.46.1.0163.shorten
dc.identifier.grantnumberEP/R015104/1en
dc.identifier.grantnumberRPG-2019-034en


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