Algebraic Numbers Satisfying Polynomials with Positive Rational Coefficients. (16th July 2014)

• Record Type: Journal Article
• Authors: Laohakosol, Vichian; Tadee, Suton
• Other Names: Laghribi Ahmed Academic Editor.
• Is Part Of: Journal of numbers. Volume 2014(2014)
• Publication Date: 2014-07-16
• Subjects: Number theory -- Periodicals; Number theory; Periodicals; 510
• DOI: 10.1155/2014/296828
• Languages: English
• ISSNs: 2356-7511

Abstract

Abstract : A theorem of Dubickas, affirming a conjecture of Kuba, states that a nonzero algebraic number is a root of a polynomialf 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 off 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.