Value sets of polynomial maps over finite fields

TL;DR

This paper establishes upper bounds on the size of the value set for multivariate polynomial maps over finite fields, extending previous bounds known for univariate cases.

Contribution

It generalizes existing bounds for univariate polynomials to multivariate polynomial maps over finite fields.

Findings

Derived new upper bounds for multivariate polynomial value sets

Extended classical bounds from univariate to multivariate cases

Provides theoretical tools for analyzing polynomial maps over finite fields

Abstract

We provide upper bounds for the cardinality of the value set of a polynomial map in several variables over a finite field. These bounds generalize earlier bounds for univariate polynomials.