Popular Differences and the Croot--Lev Half-Threshold Problem

Jianfeng Hou Wei Li, Kai Yang

Let $A$ be a finite non-empty subset of an abelian group $G$, and let $r_A(d)=|\{(a,a^{\prime })\in A^2:a-a^{\prime }=d\}|$. Croot and Lev asked whether the pointwise half-threshold condition $r_A(d…