Ben Green

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math.NT2026

Remarks on the inverse Littlewood conjecture

Thomas F. Bloom, Ben Green

The Littlewood conjecture, proven by Konyagin and McGehee-Pigno-Smith in the 1980s, states that if $A \subset Z$ is a finite set of integers with $∣ A ∣ = N$ then $\…

math.NT2024

Covering integers by $x^{2} + d y^{2}$

Ben Green, Kannan Soundararajan

What proportion of integers $n ⩽ N$ may be expressed as $x^{2} + d y^{2}$ for some $d ⩽ I^$ , with $x, y$ integers? Writing $I^$ as $(\log N)^{\log 2} 2^{Î±\sqrt{\log \lo…

Remarks on the inverse Littlewood conjecture

Covering integers by x2+dy2

Covering integers by $x^{2} + d y^{2}$