Popular sum
= Popular sum
{title2=$r_{A+A}(t)\geq u$}
A popular sum of a finite set $A$ is an element having at least a specified number $u$ of ordered representations as $a+b$, with $a,b\in A$. Popular sums define a dense <bipartite graph> when <additive energy> is large. Since the total representation count is $|A|^2$, there are at most $|A|^2/u$ popular sums.