A nonlinear version of Roth's theorem for sets of positive density in the real line
type: Item
instance of: scholarly article
title: A nonlinear version of Roth's theorem for sets of positive density in the real line
zbMATH Open document ID: 0675.42010
DOI: 10.1007/BF02796120
published in: Journal d'Analyse Mathématique
publication date: 1988-01-01T00:00:00Z
review text: The author proves that given \(\epsilon >0\) there is a \(\delta (\epsilon)>0\) such that if S is a measurable subset of [0,N], \(| S| >\epsilon N\), then there exist \(a<b<c\) in S satisfying \((c-b)=(b- a)^ 2\) and \(b-a>\delta (\epsilon)\sqrt{N}\).
Mathematics Subject Classification ID: 42A38
Mathematics Subject Classification ID: 11B83
zbMATH DE Number: 4105556
zbMATH Keywords: Fourier transforms
zbMATH Keywords: Roth's theorem
author: Jean Bourgain
reviewed by: S. M. Mazhar
MaRDI profile type: Publication
cites work: A Szemerédi type theorem for sets of positive density in \(\mathbb R^k\)
cites work: Q4720177
full work available at URL: https://doi.org/10.1007/bf02796120
OpenAlex ID: W2005734216
description: scientific article; zbMATH DE number 4105556