Additive structures in sumsets
数论
2010-04-02 v2 组合数学
摘要
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}}.
引用
@article{arxiv.math/0605520,
title = {Additive structures in sumsets},
author = {Tom Sanders},
journal= {arXiv preprint arXiv:math/0605520},
year = {2010}
}
备注
28 pp. Corrected typos. Updated references.