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Additive structures in sumsets

Tom Sanders
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Abstract

Suppose that A is a subset of the integers {1,...,N} of density a. We provide a new proof of a result of Green which shows that A+A contains an arithmetic progression of length exp(ca(log N)^{1/2}) for some absolute c>0. Furthermore we improve the length of progression guaranteed in higher sumsets; for example we show that A+A+A contains a progression of length roughly N^{ca} improving on the previous best of N^{ca^{2+ε}}.

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Tom Sanders. 2010-04-01. Additive structures in sumsets. https://doi.org/10.1017/s030500410700093x

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