Advanced Problems: 6631-6633

Evans, Ronald M.; Montgomery, Peter L.; Muraz, Gilbert; Szeptyci, Pawel; Galvin, Fred; Porta, Horácio

doi:10.2307/2324411

Cited by 3 publications

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“…It has been recently noted by R. Evans and P. Montgomery [4] that in the special case when p is the polynomial PN defined in ( 1 ) that the corresponding reduced pt polynomials are all strictly unimodal (in their coefficients). Also, R. Evans and J. Greene [3] have shown for polynomials p of the form p(z) -(zMk -l)/(z -1) that the corresponding reduced pt polynomials all have positive coefficients.…”

Section: Introductionmentioning

confidence: 99%

Polynomials with Nonnegative Coefficients

Barnard¹,

Dayawansa²,

Pearce³

et al. 1991

Proceedings of the American Mathematical Society

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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.

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Section: Introductionmentioning

confidence: 99%

Polynomials with Nonnegative Coefficients

Barnard¹,

Dayawansa²,

Pearce³

et al. 1991

Proceedings of the American Mathematical Society

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show abstract

Polynomials with nonnegative coefficients

Barnard¹,

Dayawansa²,

Pearce³

et al. 1991

Proc. Amer. Math. Soc.

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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.

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Polynomials with Nonnegative Coefficients Whose Zeros Have Modulus One

Evans¹,

Greene²

1991

SIAM J. Math. Anal.

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Advanced Problems: 6631-6633

Cited by 3 publications

References 0 publications

Polynomials with Nonnegative Coefficients

Polynomials with Nonnegative Coefficients

Polynomials with nonnegative coefficients

Polynomials with Nonnegative Coefficients Whose Zeros Have Modulus One

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