Roots and coefficients of multivariate polynomials over finite field

TL;DR

This paper extends the study of the relationship between roots and coefficient patterns from univariate polynomials to multivariate polynomials over finite fields, broadening the theoretical understanding in this area.

Contribution

It generalizes previous results on root-coefficient relations from univariate to multivariate polynomials over finite fields.

Findings

Established new relations for multivariate polynomial roots and coefficients.

Extended univariate results to multivariate cases.

Provides theoretical foundation for further research in finite field polynomials.

Abstract

Kopparty and Wang studied in [3] the relation between the roots of a univariate polhynomial over GF(q) and the zero-nonzero pattern of its coefficients. We generalize their results to polynomials in more variables.