Open AccessAn analytic approach to the degree bound in the Nullstellensatz
Author(s) -
HyunKyoung Kwon,
Anupan Netyanun,
Tavan T. Trent
Publication year - 2015
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/12781
Subject(s) - univariate , mathematics , degree (music) , upper and lower bounds , unit (ring theory) , simple (philosophy) , analytic function , ideal (ethics) , pure mathematics , mathematical analysis , physics , multivariate statistics , statistics , philosophy , mathematics education , epistemology , acoustics
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.