Ben Green

collaborators

3 papers

math.NT2026

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.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.NT2025

New bounds for the Furstenberg-SÃ¡rkÃ¶zy theorem

Ben Green, Mehtaab Sawhney

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

Primes of the form p2+nq2

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

New bounds for the Furstenberg-SÃ¡rkÃ¶zy theorem

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

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