On the Bound of Inverse Images of a Polynomial Map

Ilya Vyugin

paper

On the Bound of Inverse Images of a Polynomial Map

arXiv:1811.08930

Abstract

Let $f_{1} (x), \dots, f_{n} (x)$ be some polynomials. The upper bound on the number of $x \in F_{p}$ such that $f_{1} (x), \dots, f_{n} (x)$ are roots of unit of order $t$ is obtained. This bound generalize the bound of the paper \cite{V-S} to the case of polynomials of degrees greater than one. The bound is obtained over fields of positive characteristic and over the complex field.

10 pages