An analytic approach to the degree bound in the Nullstellensatz

Abstract

The Bezout version of Hilbert’s Nullstellensatz states that polynomials without a common zero form the unit ideal. In this paper, we start with a finite number of univariate polynomials and consider the polynomials that show up as a result of the Nullstellensatz. We present a simple analytic method of obtaining a bound for the degrees of these polynomials. Our result recovers W. D. Brownawell’s bound and is consistent with that of J. Kollár in the univariate case. The proof involves some well-known results on the analyticity of complex-valued functions.