New bounds in the Bogolyubov-Ruzsa lemma
Combinatorics
2023-11-10 v2 Number Theory
Abstract
We establish new bounds in the Bogolyubov-Ruzsa lemma, demonstrating that if A is a subset of a finite abelian group with density alpha, then 3A-3A contains a Bohr set of rank O(log^2 (2/alpha)) and radius Omega(log^{-2} (2/alpha)). The Bogolyubov-Ruzsa lemma is one of the deepest results in additive combinatorics, with a plethora of important consequences. In particular, we obtain new results toward the Polynomial Freiman-Ruzsa conjecture and improved bounds in Freiman's theorem.
Keywords
Cite
@article{arxiv.2311.04125,
title = {New bounds in the Bogolyubov-Ruzsa lemma},
author = {Tomasz Kosciuszko and Tomasz Schoen},
journal= {arXiv preprint arXiv:2311.04125},
year = {2023}
}
Comments
Mistake in Lemma 5.1