Quadratic Expansion over Prime Fields via Centered Collisions and Popular-Sum Amplification

Zhi Yao

Let $p$ be an odd prime, let $\varnothing \ne A\subseteq {\mathbb{F}}_p$ have cardinality $N$, and let $f\in {\mathbb{F}}_p[x,y]$ be a non-degenerate quadratic polynomial. Writing $S=|A+A|…