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dc.contributor.authorFraser, Jonathan
dc.contributor.authorShmerkin, Pablo
dc.contributor.authorYavicoli, Alexia
dc.date.accessioned2022-02-21T11:30:01Z
dc.date.available2022-02-21T11:30:01Z
dc.date.issued2021-02-10
dc.identifier273170185
dc.identifier13c1bdb2-7a1f-4bc0-9b39-d55685559958
dc.identifier85101026515
dc.identifier000618298800001
dc.identifier.citationFraser , J , Shmerkin , P & Yavicoli , A 2021 , ' Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions ' , Journal of Fourier Analysis and Applications , vol. 27 , no. 4 , 4 . https://doi.org/10.1007/s00041-020-09807-wen
dc.identifier.issn1069-5869
dc.identifier.otherORCID: /0000-0002-8066-9120/work/90112119
dc.identifier.urihttps://hdl.handle.net/10023/24913
dc.descriptionJMF is financially supported by an EPSRC Standard Grant (EP/R015104/1) and a Leverhulme Trust Research Project Grant (RPG-2019-034). PS is supported by a Royal Society International Exchange Grant and by Project PICT 2015-3675 (ANPCyT). AY is financially supported by the Swiss National Science Foundation, Grant No. P2SKP2_184047.en
dc.description.abstractWe provide quantitative estimates for the supremum of the Hausdorff dimension of sets in the real line which avoid ε-approximations of arithmetic progressions. Some of these estimates are in terms of Szemerédi bounds. In particular, we answer a question of Fraser, Saito and Yu (IMRN 14:4419–4430, 2019) and considerably improve their bounds. We also show that Hausdorff dimension is equivalent to box or Assouad dimension for this problem, and obtain a lower bound for Fourier dimension.
dc.format.extent14
dc.format.extent187473
dc.language.isoeng
dc.relation.ispartofJournal of Fourier Analysis and Applicationsen
dc.subjectArithmetic progressionsen
dc.subjectHausdorff dimensionen
dc.subjectFractalsen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleImproved bounds on the dimensions of sets that avoid approximate arithmetic progressionsen
dc.typeJournal articleen
dc.contributor.sponsorEPSRCen
dc.contributor.sponsorThe Leverhulme Trusten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doi10.1007/s00041-020-09807-w
dc.description.statusPeer revieweden
dc.identifier.urlhttps://arxiv.org/abs/1910.10074en
dc.identifier.grantnumberEP/R015104/1en
dc.identifier.grantnumberRPG-2019-034en


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