A structure theorem for sets with doubling $4+\hat{I}´$

Abstract

We prove a structural result for sets of integers with doubling at most $4+\hat{I}´$, with $\hat{I}´>0$ sufficiently small. This generalises earlier work of Eberhard--Green--Manners which dealt with sets of integers with doubling strictly less than $4$, and makes progress towards a question of Green.

30 pages