Ganzzahlige Gleichungen ohne Affekt
Generalizations of some irreducibility results by Schur
Generalized Kummer theory and its applications
In this report we study the arithmetic of Rikuna’s generic polynomial for the cyclic group of order and obtain a generalized Kummer theory. It is useful under the condition that and where is a primitive -th root of unity and . In particular, this result with implies the classical Kummer theory. We also present a method for calculating not only the conductor but also the Artin symbols of the cyclic extension which is defined by the Rikuna polynomial.
Generating functions of finitely generated Witt rings
Groupes totaux
Les « groupes totaux » sont les groupes pour lesquels la dimension du centre l’algèbre des invariants d’une algèbre simple centrale associée à un -cocycle sous l’action d’un relevé de l’action galoisienne à est constante quels que soient et . Dans cet article, nous montrons que les groupes quasi-CC (qui sont les groupes de centre cyclique et dont les centralisateurs des éléments hors du centre sont cycliques) sont totaux. Les groupes de type CC qui sont les groupes quasi-CC à centre trivial...
Hamburger-Noether Expansions and Approximate Roots of Polynomials.
Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory
2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20.This paper gives a characterization of Henselian discrete valued fields whose finite abelian extensions are uniquely determined by their norm groups and related essentially in the same way as in the classical local class field theory. It determines the structure of the Brauer groups and character groups of Henselian discrete valued strictly primary quasilocal (or PQL-) fields, and thereby, describes the forms of the local reciprocity...
Higher Level Reduced Witt Rings of Skew Fields.
Hilbert sets and zeta functions over finite fields.
Hilbert Subsets and s-Integral Points.
Hosszú's functional equation over rings generated by their units. (Short Communication).
Hosszú's functional equation over rings generated by their units.
Hyperquadratic power series of degree four
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...
Irreducible discriminant components of coefficient spaces
Isotropy of quadratic spaces in finite and infinite dimension.