Table of Contents
Journal of Numbers
Volume 2014 (2014), Article ID 296828, 8 pages
http://dx.doi.org/10.1155/2014/296828
Research Article

Algebraic Numbers Satisfying Polynomials with Positive Rational Coefficients

1Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand
2Department of Mathematics and Statistics, Faculty of Science and Technology, Thepsatri Rajabhat University, Lopburi 15000, Thailand

Received 2 May 2014; Accepted 30 June 2014; Published 16 July 2014

Academic Editor: Ahmed Laghribi

Copyright © 2014 Vichian Laohakosol and Suton Tadee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A theorem of Dubickas, affirming a conjecture of Kuba, states that a nonzero algebraic number is a root of a polynomial 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 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.