Solutions of polynomial equation over ${\mathbb{F}}_p$ and new bounds of additive energy

Ilya Vyugin, Sergey Makarychev

We present a new proof of Corvaja and Zannier's \cite{C-Z} the upper bound of the number of solutions $(x,y)$ of the algebraic equation $P(x,y)=0$ over a field ${\mathbb{F}}_p$ ($p$…