90 citations · 148 across the 3 of their papers we have counts for
6 papers
Marton's Conjecture in abelian groups with bounded torsion
W. T. Gowers, Ben Green, Freddie Manners +1
We prove a Freiman--Ruzsa-type theorem with polynomial bounds in arbitrary abelian groups with bounded torsion, thereby proving (in full generality) a conjecture of Marton. Specifi…
On a conjecture of Marton
W. T. Gowers, Ben Green, Freddie Manners +1
We prove a conjecture of K. Marton, widely known as the polynomial Freiman--Ruzsa conjecture, in characteristic . The argument extends to odd characteristic, with details to fol…
Sets of integers with no large sum-free subset
Sean Eberhard, Ben Green, Freddie Manners
Answering a question of P. Erdos from 1965, we show that for every eps>0 there is a set A of n integers with the following property: every subset A' of A with at least (1/3 + eps)n…
An equivalence between inverse sumset theorems and inverse conjectures for the U^3 norm
Ben Green, Terence Tao
We establish a correspondence between inverse sumset theorems (which can be viewed as classifications of approximate (abelian) groups) and inverse theorems for the Gowers norms (wh…
The Mobius function is strongly orthogonal to nilsequences
Ben Green, Terence Tao
We show that the Mobius function mu(n) is strongly asymptotically orthogonal to any polynomial nilsequence n -> F(g(n)L). Here, G is a simply-connected nilpotent Lie group with a d…
The distribution of polynomials over finite fields, with applications to the Gowers norms
Ben Green, Terence Tao
In this paper we investigate the uniform distribution properties of polynomials in many variables and bounded degree over a fixed finite field F of prime order. Our main result is…