Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Polynomials with nonnegative coefficients


Authors: R. W. Barnard, W. Dayawansa, K. Pearce and D. Weinberg
Journal: Proc. Amer. Math. Soc. 113 (1991), 77-85
MSC: Primary 30C10
MathSciNet review: 1072329
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The authors verify the conjecture that a conjugate pair of zeros can be factored from a polynomial with nonnegative coefficients so that the resulting polynomial still has nonnegative coefficients. The conjecture was originally posed by A. Rigler, S. Trimble, and R. Varga arising out of their work on the Beauzamy-Enflo generalization of Jensen's inequality. The conjecture was also made independently by B. Conroy in connection with his work in number theory. A crucial and interesting lemma is proved which describes general coefficient-root relations for polynomials with nonnegative coefficients and for polynomials for which the case of equality holds in Descarte's Rule of Signs.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30C10

Retrieve articles in all journals with MSC: 30C10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1072329-2
PII: S 0002-9939(1991)1072329-2
Article copyright: © Copyright 1991 American Mathematical Society