English

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

R2 v1 2026-06-21T11:06:24.141Z