B. Green

activity

20032026

most citedA Szemeredi-type regularity lemma in abelian groups, with applications

113 citations · 646 across the 78 of their papers we have counts for

collaborators

Showing math.NTShow all

42 papers · 1 filter

math.NT2023★ 12 cited

Sumsets and entropy revisited

Ben Green, Freddie Manners, Terence Tao

The entropic doubling $σ_{ent} [X]$ of a random variable $X$ taking values in an abelian group $G$ is a variant of the notion of the doubling constant $σ [A]$ of a fin…

math.NT2022

On Sárközy's theorem for shifted primes

Ben Green

Suppose that $A \subset {1, \dots, N}$ has no two elements differing by $p - 1$ , $p$ prime. Then $∣ A ∣ ≪ N^{1 - c}$ .

math.NT2021★ 1 cited

Quadratic forms in 8 prime variables

Ben Green

We give an asymptotic for the number of prime solutions to $Q (x_{1}, \dots, x_{8}) = N$ , subject to a mild non-degeneracy condition on the homogeneous quadratic form $Q$ . The argument i…

math.NT2020★ 3 cited

Extremal problems for GCDs

Ben Green, Aled Walker

We prove that if $A \subseteq [X, 2 X]$ and $B \subseteq [Y, 2 Y]$ are sets of integers such that $g cd (a, b) \geq D$ for at least $δ ∣ A ∣∣ B ∣$ pairs $(a, b) \in A \times B$ then $|A||B|…

math.NT2020★ 2 cited

A Weighted Prékopa-Leindler inequality and sumsets with quasicubes

Ben Green, Dávid Matolcsi, Imre Ruzsa +2

We give a short, self-contained proof of two key results from a paper of four of the authors. The first is a kind of weighted discrete Prékopa-Leindler inequality. This is then app…

math.NT2019

Equal sums in random sets and the concentration of divisors

Kevin Ford, Ben Green, Dimitris Koukoulopoulos

We study the extent to which divisors of a typical integer $n$ are concentrated. In particular, defining the Erdős-Hooley $Δ$ -function by $Δ(n) := \max_t \# \{d | n, \log d \in [t,…