Generalizing the Chevalley-Warning Theorem

Abstract

The Chevalley-Warning Theorem states that a set of polynomials over a finite field without constant terms has a non-trivial common zero if the number of variables exceeds the sum of the degrees. In this report, we will prove the Chevalley-Warning Theorem along with one of its generalizations. This will be done by using the Combinatorial Nullstellensatz.