Fields containing values of algebraic functions II (On a conjecture of Schinzel)
Functional equations stemming from numerical analysis [Book]
Generalizations of some irreducibility results by Schur
Hamburger-Noether Expansions and Approximate Roots of Polynomials.
Image sets of polynomials
Improvements on the Cantor-Zassenhaus factorization algorithm
The paper presents a careful analysis of the Cantor-Zassenhaus polynomial factorization algorithm, thus obtaining tight bounds on the performances, and proposing useful improvements. In particular, a new simplified version of this algorithm is described, which entails a lower computational cost. The key point is to use linear test polynomials, which not only reduce the computational burden, but can also provide good estimates and deterministic bounds of the number of operations needed for factoring....
Indecomposable polynomials and their spectrum
Inégalités sur la mesure de Mahler d'un polynôme
Dans cet article, nous donnons une minoration de la mesure de Mahler d'un polynôme à coefficients entiers, dont toutes les racines sont d'une part réelles positives, d'autre part réelles, en fonction de la valeur de ce polynôme en zéro. Ces minorations améliorent des résultats antérieurs de A. Schinzel. Par ailleurs, nous en déduisons des inégalités de M.-J. Bertin, liant la mesure d'un nombre algébrique à sa norme.
Irreducibility of the iterates of a quadratic polynomial over a field
1. Introduction. Let K be a field of characteristic p ≥ 0 and let f(X) be a polynomial of degree at least two with coefficients in K. We set f₁(X) = f(X) and define for all r ≥ 1. Following R. W. K. Odoni [7], we say that f is stable over K if is irreducible over K for every r ≥ 1. In [6] the same author proved that the polynomial f(X) = X² - X + 1 is stable over ℚ. He wrote in [7] that the proof given there is quite difficult and it would be of interest to have an elementary proof. In the sequel...
La propriété des corps
Linear relations between roots of polynomials
Localisation des zéros de polynômes par rapport au cercle unité
Localisation des zéros de polynômes réciproques
Minimal degree solutions of polynomial equations
Mosco convergence of sequences of homogeneous polynomials.
In this paper we give a characterization of uniform convergence on weakly compact sets, for sequences of homogeneous polynomials in terms of the Mosco convergence of their level sets. The result is partially extended for holomorphic functions. Finally we study the relationship with other convergences.
New inequalities on polynomial divisors.
Newton-Puiseux expansion and generalized Tschirnhausen transformation. I.
Noether forms for the study of non-composite rational functions and their spectrum
Nonstandard arithmetic of iterated polynomials.
On a conjecture of Davenport and Lewis concerning exceptional polynomials