Salem Sets with No Arithmetic Progressions

dc.creatorShmerkin, Pablo Sebastian
dc.date.accessioned2019-03-26T22:20:09Z
dc.date.accessioned2022-10-14T21:35:06Z
dc.date.available2019-03-26T22:20:09Z
dc.date.available2022-10-14T21:35:06Z
dc.date.created2019-03-26T22:20:09Z
dc.date.issued2017-04
dc.identifierShmerkin, Pablo Sebastian; Salem Sets with No Arithmetic Progressions; Oxford University Press; International Mathematics Research Notices; 2017; 7; 4-2017; 1929-1941
dc.identifier1073-7928
dc.identifierhttp://hdl.handle.net/11336/72608
dc.identifierCONICET Digital
dc.identifierCONICET
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/4309249
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.
dc.languageeng
dc.publisherOxford University Press
dc.relationinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1510.07596
dc.relationinfo:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1093/imrn/rnw097
dc.relationinfo:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imrn/article-abstract/2017/7/1929/3060565
dc.rightshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectARITHMETIC PROGRESSIONS
dc.subjectSALEM SETS
dc.subjectPSEUDO-RANDOMNESS
dc.titleSalem Sets with No Arithmetic Progressions
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:ar-repo/semantics/artículo
dc.typeinfo:eu-repo/semantics/publishedVersion


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