A nonlinear version of Roth's theorem for sets of positive density in the real line (Q1122088)
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scientific article; zbMATH DE number 4105556
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A nonlinear version of Roth's theorem for sets of positive density in the real line |
scientific article; zbMATH DE number 4105556 |
Statements
A nonlinear version of Roth's theorem for sets of positive density in the real line (English)
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1988
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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 \(b-a>\delta (\epsilon)\sqrt{N}\).
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Fourier transforms
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Roth's theorem
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