Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

An analytic approach to the degree bound in the Nullstellensatz


Authors: Hyun-Kyoung Kwon, Anupan Netyanun and Tavan T. Trent
Journal: Proc. Amer. Math. Soc. 144 (2016), 1145-1152
MSC (2010): Primary 30H05; Secondary 30J99, 46J20, 32A65, 30D20, 30H80
DOI: https://doi.org/10.1090/proc/12781
Published electronically: October 20, 2015
MathSciNet review: 3447667
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 30H05, 30J99, 46J20, 32A65, 30D20, 30H80

Retrieve articles in all journals with MSC (2010): 30H05, 30J99, 46J20, 32A65, 30D20, 30H80


Additional Information

Hyun-Kyoung Kwon
Affiliation: Department of Mathematics, The University of Alabama, Box 870350, Tuscaloosa, Alabama 35401
Email: hkwon@ua.edu

Anupan Netyanun
Affiliation: Department of Mathematics, The University of Alabama, Box 870350, Tuscaloosa, Alabama 35401
Email: sdiff99@hotmail.com

Tavan T. Trent
Affiliation: Department of Mathematics, The University of Alabama, Box 870350, Tuscaloosa, Alabama 35401
Email: ttrent@ua.edu

DOI: https://doi.org/10.1090/proc/12781
Received by editor(s): October 10, 2014
Received by editor(s) in revised form: December 20, 2014, and February 15, 2015
Published electronically: October 20, 2015
Communicated by: Pamela B. Gorkin
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society