Ben Green

activity

20042025

most citedFinite field models in additive combinatorics

7 citations · 7 across the 4 of their papers we have counts for

collaborators

4 papers

math.NT2025

Bounds for monochromatic solutions to ${x + y, x y}$

Ben Green, Mehtaab Sawhney

Let $r$ be a sufficiently large positive integer, and let $N \geq exp exp (r^{50})$ . Then any $r$ -colouring of $[N]$ contains a monochromatic copy of ${x + y, x y}$ with $x > y > 2$ .

math.NT2024

New bounds for the Furstenberg-Sárközy theorem

Ben Green, Mehtaab Sawhney

Suppose that $A \subset {1, \dots, N}$ has no two elements differing by a square. Then $∣ A ∣ ≪ N e^{- c l o g N}$ .

math.NT2024

Primes of the form $p^{2} + n q^{2}$

Ben Green, Mehtaab Sawhney

Suppose that $n$ is $0$ or $4$ modulo $6$ . We show that there are infinitely many primes of the form $p^{2} + n q^{2}$ with both $p$ and $q$ prime, and obtain an asymptotic for their nu…

math.NT2004★ 7 cited

Finite field models in additive combinatorics

Ben Green

The study of many problems in additive combinatorics, such as Szemerédi's theorem on arithmetic progressions, is made easier by first studying models for the problem in F_p^n for s…

Bounds for monochromatic solutions to {x+y,xy}

New bounds for the Furstenberg-Sárközy theorem

Primes of the form p2+nq2

Finite field models in additive combinatorics

Bounds for monochromatic solutions to ${x + y, x y}$

Primes of the form $p^{2} + n q^{2}$