Control and its applications in additive combinatorics
Number Theory
2025-01-17 v1 Combinatorics
Abstract
We prove new quantitative bounds on the additive structure of sets obeying an 'control' assumption, which arises naturally in several questions within additive combinatorics. This has a number of applications - in particular we improve the known bounds for the sum-product problem, the Balog-Szemer\'{e}di-Gowers theorem, and the additive growth of convex sets.
Cite
@article{arxiv.2501.09470,
title = {Control and its applications in additive combinatorics},
author = {Thomas F. Bloom},
journal= {arXiv preprint arXiv:2501.09470},
year = {2025}
}
Comments
28 pages