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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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