Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions

Autores
Fraser, Jonathan M.; Shmerkin, Pablo Sebastian; Yavicoli, Alexia
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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.
Fil: Fraser, Jonathan M.. University of St. Andrews; Reino Unido
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
Fil: Yavicoli, Alexia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. University of St. Andrews; Reino Unido
Materia
ARITHMETIC PROGRESSIONS
FRACTALS
HAUSDORFF DIMENSION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/164764
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/164764
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Improved bounds on the dimensions of sets that avoid approximate arithmetic progressionsFraser, Jonathan M.Shmerkin, Pablo SebastianYavicoli, AlexiaARITHMETIC PROGRESSIONSFRACTALSHAUSDORFF DIMENSIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We 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.Fil: Fraser, Jonathan M.. University of St. Andrews; Reino UnidoFil: 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; CanadáFil: Yavicoli, Alexia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. University of St. Andrews; Reino UnidoBirkhauser Boston Inc2021-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/164764Fraser, 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; 1-141069-58691531-5851CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00041-020-09807-winfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-020-09807-winfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1910.10074v3info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:34:29Zoai:ri.conicet.gov.ar:11336/164764instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:34:29.377CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions
title Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions
spellingShingle Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions
Fraser, Jonathan M.
ARITHMETIC PROGRESSIONS
FRACTALS
HAUSDORFF DIMENSION
title_short Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions
title_full Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions
title_fullStr Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions
title_full_unstemmed Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions
title_sort Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions
dc.creator.none.fl_str_mv Fraser, Jonathan M.
Shmerkin, Pablo Sebastian
Yavicoli, Alexia
author Fraser, Jonathan M.
author_facet Fraser, Jonathan M.
Shmerkin, Pablo Sebastian
Yavicoli, Alexia
author_role author
author2 Shmerkin, Pablo Sebastian
Yavicoli, Alexia
author2_role author
author
dc.subject.none.fl_str_mv ARITHMETIC PROGRESSIONS
FRACTALS
HAUSDORFF DIMENSION
topic ARITHMETIC PROGRESSIONS
FRACTALS
HAUSDORFF DIMENSION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv 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.
Fil: Fraser, Jonathan M.. University of St. Andrews; Reino Unido
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
Fil: Yavicoli, Alexia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. University of St. Andrews; Reino Unido
description 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.
publishDate 2021
dc.date.none.fl_str_mv 2021-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/164764
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
1069-5869
1531-5851
CONICET Digital
CONICET
url http://hdl.handle.net/11336/164764
identifier_str_mv 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
1069-5869
1531-5851
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00041-020-09807-w
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-020-09807-w
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1910.10074v3
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Birkhauser Boston Inc
publisher.none.fl_str_mv Birkhauser Boston Inc
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1844613066856071168
score 13.070432

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