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dc.contributor.author
Fraser, Jonathan M.  
dc.contributor.author
Shmerkin, Pablo Sebastian  
dc.contributor.author
Yavicoli, Alexia  
dc.date.available
2022-08-09T14:15:57Z  
dc.date.issued
2021-02  
dc.identifier.citation
Fraser, Jonathan M.; Shmerkin, Pablo Sebastian; Yavicoli, Alexia; Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions; Birkhauser Boston Inc; Journal Of Fourier Analysis And Applications; 27; 1; 2-2021; 1-14  
dc.identifier.issn
1069-5869  
dc.identifier.uri
http://hdl.handle.net/11336/164764  
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
application/pdf  
dc.language.iso
eng  
dc.publisher
Birkhauser Boston Inc  
dc.rights
info:eu-repo/semantics/openAccess  
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/  
dc.subject
ARITHMETIC PROGRESSIONS  
dc.subject
FRACTALS  
dc.subject
HAUSDORFF DIMENSION  
dc.subject.classification
Matemática Pura  
dc.subject.classification
Matemáticas  
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS  
dc.title
Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions  
dc.type
info:eu-repo/semantics/article  
dc.type
info:ar-repo/semantics/artículo  
dc.type
info:eu-repo/semantics/publishedVersion  
dc.date.updated
2022-08-04T15:33:44Z  
dc.identifier.eissn
1531-5851  
dc.journal.volume
27  
dc.journal.number
1  
dc.journal.pagination
1-14  
dc.journal.pais
Estados Unidos  
dc.journal.ciudad
Boston  
dc.description.fil
Fil: Fraser, Jonathan M.. University of St. Andrews; Reino Unido  
dc.description.fil
Fil: Shmerkin, Pablo Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. University of British Columbia; Canadá  
dc.description.fil
Fil: Yavicoli, Alexia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. University of St. Andrews; Reino Unido  
dc.journal.title
Journal Of Fourier Analysis And Applications  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00041-020-09807-w  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s00041-020-09807-w  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1910.10074v3  

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