Algebraic Numbers Satisfying Polynomials with Positive Rational Coefficients
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A theorem of Dubickas, affirming a conjecture of Kuba, states that a nonzero algebraic number is a root of a polynomial f with positive rational coefficients if and only if none of its conjugates is a positive real number. A certain quantitative version of this result, yielding a growth factor for the coefficients of f similar to the condition of the classical Eneström-Kakeya theorem of such polynomial, is derived. The bound for the growth factor so obtained is shown to be sharp for some particular classes of algebraic numbers.
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2018 ◽
Vol 7
(1)
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pp. 77-83
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2014 ◽
Vol 16
(04)
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pp. 1350046
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1989 ◽
Vol 26
(01)
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pp. 103-112
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1964 ◽
Vol 4
(1)
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pp. 122-128
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