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Polynomials with Nonnegative Coefficients
R. W. Barnard, W. Dayawansa, K. Pearce and D. Weinberg
Proceedings of the American Mathematical Society
Vol. 113, No. 1 (Sep., 1991), pp. 77-85
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2048441
Page Count: 9
You can always find the topics here!Topics: Polynomials, Coefficients, Algebraic conjugates, Mathematical inequalities, Number theory, Mathematical theorems, Multiplicity of function roots, Zero, Critical points, Integers
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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.
Proceedings of the American Mathematical Society © 1991 American Mathematical Society