EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 89(103), pp. 89–93 (2011)

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ON ROOTS OF POLYNOMIALS
WITH POSITIVE COEFFICIENTS

Toufik Za\"{i}mi

Department of Mathematics, Larbi Ben M'hidi University, Oum El Bouaghi 04000, Algeria

Abstract: Let $\alpha $ be an algebraic number with no nonnegative conjugates over the field of the rationals. Settling a recent conjecture of Kuba, Dubickas proved that the number $\alpha$ is a root of a polynomial, say $P$, with positive rational coefficients. We give in this note an upper bound for the degree of $P$ in terms of the discriminant, the degree and the Mahler measure of $\alpha$; this answers a question of Dubickas.

Classification (MSC2000): 11R04; 12D10; 11R06

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Electronic fulltext finalized on: 6 Apr 2011. This page was last modified: 16 Oct 2012.

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