doiSerbia

On roots of polynomials with positive coefficients

Zaïmi Toufik (Department of Mathematics, Larbi Ben M’hidi University, Oum El Bouaghi, Algeria)

Let α 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 α 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 α; this answers a question of Dubickas.