A Schwartz-Zippel Type Estimate for Homogenous Finite Field Polynomials

In this paper, we obtain a Schwartz-Zippel type estimate for homogenous finite field polynomials. Specifically, we use a probabilistic recursion technique to find upper and lower bounds for the number of zeros of a homogenous polynomial and illustrate our result with two examples involving perfect matching in bipartite graphs and common zeros in a collection of polynomials, respectively.