Salem Sets with No Arithmetic Progressions

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dc.conicet.fuenteindividual
dc.conicet.organizacionUniversidad Torcuato Di Tella. Departamento de Matemáticas y Estadística
dc.conicet.organizacionConsejo Nacional de Investigaciones Científicas y Técnicas
dc.conicet.paisOrganizacionArgentina
dc.conicet.paisOrganizacionArgentina
dc.conicet.produccionid6987639
dc.contributor.authorShmerkin, Pablo Sebastian
dc.date.accessioned2019-03-26T22:20:09Z
dc.date.available2019-03-26T22:20:09Z
dc.date.issued2017-04
dc.date.updated2019-03-26T13:58:16Z
dc.description.abstractWe construct compact Salem sets in R/Z of any dimension (including 1), which do not contain any arithmetic progressions of length 3. Moreover, the sets can be taken to be Ahlfors regular if the dimension is less than 1, and the measure witnessing the Fourier decay can be taken to be Frostman in the case of dimension 1. This is in sharp contrast to the situation in the discrete setting (where Fourier uniformity is well known to imply existence of progressions) and helps clarify a result of Łaba and Pramanik on pseudo-random subsets of R which do contain progressions.es
dc.description.filFil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
dc.formatapplication/pdfes
dc.identifier.citationShmerkin, Pablo Sebastian; Salem Sets with No Arithmetic Progressions; Oxford University Press; International Mathematics Research Notices; 2017; 7; 4-2017; 1929-1941es
dc.identifier.institucionalCONICET
dc.identifier.issn1073-7928es
dc.identifier.repoCONICET Digital
dc.identifier.urihttp://hdl.handle.net/11336/72608
dc.journal.ciudadOxfordes
dc.journal.number7es
dc.journal.pagination1929-1941es
dc.journal.paisReino Unidoes
dc.journal.titleInternational Mathematics Research Noticeses
dc.journal.volume2017es
dc.language.isoenges
dc.publisherOxford University Presses
dc.relation.alternativeidinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1510.07596
dc.relation.alternativeidinfo:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1093/imrn/rnw097
dc.relation.alternativeidinfo:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imrn/article-abstract/2017/7/1929/3060565
dc.rightsinfo:eu-repo/semantics/openAccess*
dc.rights.urihttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/*
dc.subjectArithmetic Progressionses
dc.subjectSalem Setses
dc.subjectPseudo-Randomnesses
dc.subject.classificationMatemática Puraes
dc.subject.classificationMatemáticases
dc.subject.classificationCIENCIAS NATURALES Y EXACTASes
dc.titleSalem Sets with No Arithmetic Progressionses
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:ar-repo/semantics/artículo
dc.typeinfo:eu-repo/semantics/publishedVersion

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