Exponential sum estimates over prime fields

TL;DR

This paper extends recent results on exponential sum estimates over prime fields by analyzing polynomial energies in multiple variables, providing new bounds for character sums.

Contribution

It introduces novel bounds for multiple character sums over prime fields using polynomial energy methods, expanding previous work by Shkredov and Shparlinski.

Findings

New bounds for multiple character sums over prime fields

Extended results for polynomial energies in two and three variables

Improved estimates for exponential sums in prime fields

Abstract

In this paper, we prove some extensions of recent results given by Shkredov and Shparlinski on multiple character sums for some general families of polynomials over prime fields. The energies of polynomials in two and three variables are our main ingredients.