On roots of polynomials with positive coefficients | Zendy

Toufik Zaı̈mi | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

On roots of polynomials with positive coefficients

Author(s) -

Toufik Zaı̈mi

Publication year - 2011

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim1103089z

Subject(s) - mathematics , discriminant , degree (music) , conjecture , rational number , combinatorics , polynomial , algebraic number , root (linguistics) , discrete mathematics , pure mathematics , mathematical analysis , physics , computer science , linguistics , philosophy , artificial intelligence , acoustics

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.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research