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 2021Show all

3 papers · 1 filter

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.CO2021★ 2 cited

Lower bounds for corner-free sets

Ben Green

A corner is a set of three points in $Z^{2}$ of the form $(x, y), (x + d, y), (x, y + d)$ with $d \neq = 0$ . We show that for infinitely many $N$ there is a set $A \subset [N]…

math.CO2021★ 1 cited

New lower bounds for van der Waerden numbers

Ben Green

We show that there is a red-blue colouring of $[N]$ with no blue 3-term arithmetic progression and no red arithmetic progression of length $e^{C (l o g N)^{3/4} (l o g l o g N)^{1/4}}$ .…