Artículo
Salem Sets with No Arithmetic Progressions
Fecha de publicación:
04/2017
Editorial:
Oxford University Press
Revista:
International Mathematics Research Notices
ISSN:
1073-7928
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
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.
Palabras clave:
Arithmetic Progressions
,
Salem Sets
,
Pseudo-Randomness
Archivos asociados
Licencia
Identificadores
Colecciones
Articulos(SEDE CENTRAL)
Articulos de SEDE CENTRAL
Articulos de SEDE CENTRAL
Citación
Shmerkin, Pablo Sebastian; Salem Sets with No Arithmetic Progressions; Oxford University Press; International Mathematics Research Notices; 2017; 7; 4-2017; 1929-1941
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