Functions with large additive energy supported on a Hamming Sphere

Abstract

In this note, we prove that, among functions $f$ supported on a Hamming Sphere in ${\mathbb{F}}_2^n$ with fixed ${\ell }^2$ norm, the additive energy is maximised when $f$ is constant. This answers a question asked by Kirshner and Samorodnitsky.

3 pages