Control and its applications in additive combinatorics
Abstract
We prove new quantitative bounds on the additive structure of sets obeying an L3 '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\'edi-Gowers theorem, and the additive growth of convex sets.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.