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Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions
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dc.contributor.author | Fraser, Jonathan | |
dc.contributor.author | Shmerkin, Pablo | |
dc.contributor.author | Yavicoli, Alexia | |
dc.date.accessioned | 2022-02-21T11:30:01Z | |
dc.date.available | 2022-02-21T11:30:01Z | |
dc.date.issued | 2021-02-10 | |
dc.identifier | 273170185 | |
dc.identifier | 13c1bdb2-7a1f-4bc0-9b39-d55685559958 | |
dc.identifier | 85101026515 | |
dc.identifier | 000618298800001 | |
dc.identifier.citation | Fraser , 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-w | en |
dc.identifier.issn | 1069-5869 | |
dc.identifier.other | ORCID: /0000-0002-8066-9120/work/90112119 | |
dc.identifier.uri | https://hdl.handle.net/10023/24913 | |
dc.description | JMF 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.abstract | We 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.extent | 14 | |
dc.format.extent | 187473 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of Fourier Analysis and Applications | en |
dc.subject | Arithmetic progressions | en |
dc.subject | Hausdorff dimension | en |
dc.subject | Fractals | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.sponsor | The Leverhulme Trust | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | 10.1007/s00041-020-09807-w | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | https://arxiv.org/abs/1910.10074 | en |
dc.identifier.grantnumber | EP/R015104/1 | en |
dc.identifier.grantnumber | RPG-2019-034 | en |
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