On a theorem of Shkredov
Classical Analysis and ODEs
2011-01-28 v2
Abstract
We show that if A is a finite subset of an abelian group with additive energy at least c|A|^3 then there is a subset L of A with |L|=O(c^{-1}\log |A|) such that |A \cap Span(L)| >> c^{1/3}|A|.
Keywords
Cite
@article{arxiv.0807.5100,
title = {On a theorem of Shkredov},
author = {Tom Sanders},
journal= {arXiv preprint arXiv:0807.5100},
year = {2011}
}
Comments
5 pp. Included refinement from c^{1/2} to c^{1/3}, independently discovered by Shkredov and Yekhanin in arXiv:1004.2294. Corrected typos