Orderings under field extensions.
Ordre de transcendance sur
Polynomial subfields of k (x).
Propriété Ci revue et généralisée
Rational summation of rational functions.
Remarks on existentially closed fields and diophantine equations
Residual transcedental extensions of a valuation.
Some algebraic aspects of quadratic forms over fields of characteristic two.
Subfields of cyclic p-extensions of K(x).
Théories de Galois différentielles et transcendance
On décrit des preuves galoisiennes des versions logarithmique et exponentielle de la conjecture de Schanuel, pour les variétés abéliennes sur un corps de fonctions.
Trace functions and Galois invariant p-adic measures.
Transcendence results on the generating functions of the characteristic functions of certain self-generating sets, II
This article continues a previous paper by the authors. Here and there, the two power series F(z) and G(z), first introduced by Dilcher and Stolarsky and related to the so-called Stern polynomials, are studied analytically and arithmetically. More precisely, it is shown that the function field ℂ(z)(F(z),F(z⁴),G(z),G(z⁴)) has transcendence degree 3 over ℂ(z). This main result contains the algebraic independence over ℂ(z) of G(z) and G(z⁴), as well as that of F(z) and F(z⁴). The first statement is...
Twisted Pfister forms.
Über Hilbertsche Körper.
Un contre-exemple à une conjecture d'E. Noether
Un exemple de groupe de Galois d'une extension transcendante
Waring's problem for fields
If K is a field, denote by P(K,k) the a ∈ K which are sums of kth powers of elements of K, by P⁺(K,k) the set of a ∈ K which are sums of kth powers of totally positive elements of K. We give some simple conditions for which there exist integers w(K,k) and g(K,k) such that: a ∈ P(K,k) implies that a is the sum of at most w(K,k) kth powers; a ∈ P⁺(K,k) implies that a is the sum of at most g(K,k) totally positive kth powers. We apply the results to characterise functions that are sums of kth powers...
Zum Einbettungsproblem der algebraischen Zahlentheorie mit nicht abelschem Kern.
Zur Charakterisierung primärer Körpererweiterungen durch den Stellenbegriff.
Zur spezialisierungstheoretischen Charakterisierung der Freiheit und phi-Freiheit