Asymptotics for the number of directions determined by $[n]\times [n]$ in ${\mathbb{F}}_p^2$

Greg Martin, Ethan Patrick White, Chi Hoi Yip

Let $p$ be a prime and $n$ a positive integer such that $\sqrt{\frac{p}{2}}+1\le n\le \sqrt{p}$. For any arithmetic progression $A$ of length $n$ in ${\mathbb{F}}_p$, we establish…