Additive structures in sumsets

Details Additive structures in sumsets Additive structures in sumsets

2006-05-18

arxiv.org/abs/math/0605520v2

Math. Proc. Cambridge Philos. Soc. 144 (2008), no. 2, 289--316

Mathematics

Number Theory

28 pp. Corrected typos. Updated references.

Scientific paper

10.1017/S030500410700093X

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+\epsilon}}.

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