Sets with large additive energy and symmetric sets
Combinatorics
2010-04-15 v1
Abstract
We show that for any set A in a finite Abelian group G that has at least c |A|^3 solutions to a_1 + a_2 = a_3 + a_4, where a_i belong A there exist sets A' in A and L in G, |L| \ll c^{-1} log |A| such that A' is contained in Span of L and A' has approximately c |A|^3 solutions to a'_1 + a'_2 = a'_3 + a'_4, where a'_i belong A'. We also study so-called symmetric sets or, in other words, sets of large values of convolution.
Cite
@article{arxiv.1004.2294,
title = {Sets with large additive energy and symmetric sets},
author = {Ilya Shkredov and Sergey Yekhanin},
journal= {arXiv preprint arXiv:1004.2294},
year = {2010}
}