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dc.contributor.author
Shmerkin, Pablo Sebastian  
dc.date.available
2019-03-26T22:20:09Z  
dc.date.issued
2017-04  
dc.identifier.citation
Shmerkin, Pablo Sebastian; Salem Sets with No Arithmetic Progressions; Oxford University Press; International Mathematics Research Notices; 2017; 7; 4-2017; 1929-1941  
dc.identifier.issn
1073-7928  
dc.identifier.uri
http://hdl.handle.net/11336/72608  
dc.description.abstract
We 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.  
dc.format
application/pdf  
dc.language.iso
eng  
dc.publisher
Oxford University Press  
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
Salem Sets  
dc.subject
Pseudo-Randomness  
dc.subject.classification
Matemática Pura  
dc.subject.classification
Matemáticas  
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS  
dc.title
Salem Sets with No 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
2019-03-26T13:58:16Z  
dc.journal.volume
2017  
dc.journal.number
7  
dc.journal.pagination
1929-1941  
dc.journal.pais
Reino Unido  
dc.journal.ciudad
Oxford  
dc.description.fil
Fil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina  
dc.journal.title
International Mathematics Research Notices  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1510.07596  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1093/imrn/rnw097  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imrn/article-abstract/2017/7/1929/3060565  

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