Three-term arithmetic progressions and sumsets
arXiv:math/0611304 · doi:10.1017/S0013091506001398
Abstract
Suppose that G is an abelian group and A is a finite subset of G containing no three-term arithmetic progressions. We show that |A+A| >> |A|(log |A|)^{1/3-ε} for all ε>0.
20 pp. Corrected typos. Updated references. Corrected proof of Theorem 5.1. Minor revisions.