Equivalence of polynomial conjectures in additive combinatorics
Combinatorics
2010-01-20 v1 Number Theory
Abstract
We study two conjectures in additive combinatorics. The first is the polynomial Freiman-Ruzsa conjecture, which relates to the structure of sets with small doubling. The second is the inverse Gowers conjecture for , which relates to functions which locally look like quadratics. In both cases a weak form, with exponential decay of parameters is known, and a strong form with only a polynomial loss of parameters is conjectured. Our main result is that the two conjectures are in fact equivalent.
Keywords
Cite
@article{arxiv.1001.3356,
title = {Equivalence of polynomial conjectures in additive combinatorics},
author = {Shachar Lovett},
journal= {arXiv preprint arXiv:1001.3356},
year = {2010}
}