Iterated differences sets, Diophantine approximations and applications
type: Item
instance of: scholarly article
title: Iterated differences sets, Diophantine approximations and applications
author: Rigoberto Zelada
author: V. Bergelson
published in: Journal of Combinatorial Theory. Series A
publication date: 2021-08-25T00:00:00Z
full work available at URL: https://arxiv.org/abs/2010.02325
review text: Iterated difference sets are used to give new results about the set of \(n\in\mathbb{N}\) on which the values of an `odd real' polynomial (that is, a polynomial involving only odd powers) lie within a fixed distance of \(\mathbb{Z}\). These Diophantine results are then applied in both ergodic theory to give a new characterization of the fundamental weak mixing property and in combinatorial number theory to find a new variant of the Furstenberg-Sárközy theorem.
reviewed by: Thomas B. Ward
Mathematics Subject Classification ID: 11B30
Mathematics Subject Classification ID: 03E75
Mathematics Subject Classification ID: 05D10
Mathematics Subject Classification ID: 11B75
Mathematics Subject Classification ID: 11J83
Mathematics Subject Classification ID: 37A44
zbMATH DE Number: 7385238
zbMATH Keywords: Ramsey theory
zbMATH Keywords: Diophantine approximations
zbMATH Keywords: ergodic theory
zbMATH Keywords: ultrafilters
MaRDI profile type: Publication
Wikidata QID: Q114162665
OpenAlex ID: W3188114045
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DOI: 10.1016/J.JCTA.2021.105520
description: scientific article; zbMATH DE number 7385238