A Condition for a Polynomial Map to be Invertible.
A criterion for rational places over local fields.
A really elementary proof of real Lüroth's theorem.
Classical Lüroth theorem states that every subfield K of K(t), where t is a transcendental element over K, such that K strictly contains K, must be K = K(h(t)), for some non constant element h(t) in K(t). Therefore, K is K-isomorphic to K(t). This result can be proved with elementary algebraic techniques, and therefore it is usually included in basic courses on field theory or algebraic curves. In this paper we study the validity of this result under weaker assumptions: namely, if K is a subfield...
A weakening of the euclidean property for integral domains and applications to algebraic number theory. II.
An Analogue of Artin-Schreier Theorem.
An explicit formula for the Mahler measure of a family of -variable polynomials
An explicit formula for the Mahler measure of the -variable Laurent polynomial is given, in terms of dilogarithms and trilogarithms.
An infinite companion matrix
Analytic Continuation of Currents and Division Problems.
Bemerkungen zur Theorie der formal p-adischen Körper
Berichtigung zu der Arbeit: On Algebraic Curves over Real Closed Fields. Math. Z. 150, 49-70 (1976).
Cohomologie des groupes et corps d'invariants multiplicatifs.
Comparison of L¹- and -norms of squares of polynomials
Construction des extensions galoisiennes non abéliennes d'ordre pq ( p et q premiers) du corps des rationnels
Démonstration de la continuité des racines d'une équation algébrique
Die Zerlegungscharaktere abelscher total reeller Erweiterungen reeller Funktionenkörper einer Variablen.
Discussion de la fraction
Divisibilité du nombre de classes des corps abéliens réels.
Estensioni di una struttura paracomplessa su un corpo algebricamente chiuso ad un suo ampliamento trascendente semplice
Euklidische Körper und euklidische Hüllen von Körpern.
Extension of the Two-Variable Pierce-Birkhoff conjecture to generalized polynomials
Let be a continuous, piecewise-polynomial function. The Pierce-Birkhoff conjecture (1956) is that any such is representable in the form , for some finite collection of polynomials . (A simple example is .) In 1984, L. Mahé and, independently, G. Efroymson, proved this for ; it remains open for . In this paper we prove an analogous result for “generalized polynomials” (also known as signomials), i.e., where the exponents are allowed to be arbitrary real numbers, and not just natural numbers;...