Artículo

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

Fraser, Jonathan M.; Shmerkin, Pablo SebastianIcon ; Yavicoli, AlexiaIcon
Fecha de publicación: 02/2021
Editorial: Birkhauser Boston Inc
Revista: Journal Of Fourier Analysis And Applications
ISSN: 1069-5869
e-ISSN: 1531-5851
Idioma: Inglés
Tipo de recurso: Artículo publicado
Clasificación temática:

Resumen

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.
Palabras clave: ARITHMETIC PROGRESSIONS , FRACTALS , HAUSDORFF DIMENSION
 
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info:eu-repo/semantics/openAccess Excepto donde se diga explícitamente, este item se publica bajo la siguiente descripción: Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Unported (CC BY-NC-SA 2.5)
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URI: http://hdl.handle.net/11336/164764
URL: https://link.springer.com/article/10.1007/s00041-020-09807-w
DOI: http://dx.doi.org/10.1007/s00041-020-09807-w
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Citación
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
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