An explicit incidence theorem in F_p

Harald Andres Helfgott, Misha Rudnev

Let $P=A\times A\subset {\mathbb{F}}_p\times {\mathbb{F}}_p$, $p$ a prime. Assume that $P=A\times A$ has $n$ elements, $n<p$. See $P$ as a set of points in the plane over $\mathbb…