Corrigendum to the paper "On a theorem of Bauer and some of its applications" (Acta Arithmetica 11 (1966), pp. 333-344)
Counting exceptional units.
Das spezielle Reziprozitätsgesetz im relativbiquadratischen Zahlkörper
Décomposition des nombres premiers dans certaines extensions non abéliennes de
Décomposition des nombres premiers dans des extensions non abéliennes
Soit un corps de nombre galoisien non abélien sur dont le groupe de Galois possède un sous-groupe abélien distingué vérifiant les propriétés suivantes : l’ordre de est impair si son corps des invariants est un corps réel de degré strictement supérieur à 2, et l’application transfert qui lui est associée est l’application triviale. On montre que la décomposition d’un nombre premier dans une telle extension dépend de la représentation de ce nombre par certaines formes à coefficients entiers...
Determination of all non-normal quartic CM-fields and of all non-abelian normal octic CM-fields with class number one
Determination of the imaginary normal octic number fields with class number one which are not CM-fields
Die singulären Werte der Weberschen Funktionen f, f1, f2, ...2, ...3.
Dihedral and cyclic extensions with large class numbers
This paper is a continuation of [2]. We construct unconditionally several families of number fields with large class numbers. They are number fields whose Galois closures have as the Galois groups, dihedral groups , , and cyclic groups , . We first construct families of number fields with small regulators, and by using the strong Artin conjecture and applying some modification of zero density result of Kowalski-Michel, we choose subfamilies such that the corresponding -functions are zero free...
Ein neuer beweis für die Reziprozitätsformel der Gaußschen Summen in beliebigen algebraischen Zahlkörpern
Éléments de norme 1 des corps cubiques non galoisiens. Généralisation
Erratum à l'article „Sur les systèmes complets de restes modulo les idéaux d'un corps de nombres" Acta Arithmetica 22 (1972), pp. 49-56
Euclidean fields having a large Lenstra constant
Based on a method of H. W. Lenstra Jr. in this note 143 new Euclidean number fields are given of degree and 10 and of unit rank . The search for these examples also revealed several other fields of small discriminant compared with the lower bounds of Odlyzko.
Existence et construction des extensions galoisiennes et non-abéliennes de degré 8 d'un corps de caractéristique differente de 2.
Frobenius distributions for real quadratic orders
We present a density result for the norm of the fundamental unit in a real quadratic order that follows from an equidistribution assumption for the infinite Frobenius elements in the class groups of these orders.
Fundamental units in a parametric family of not totally real quintic number fields
In this article we compute fundamental units for a family of number fields generated by a parametric polynomial of degree 5 with signature and Galois group .
Geschlechtertheorie der Ringklassenkörper.
Global restrictions on ramification in number fields.
Hasse's Class Number Product Formula for Generalized Dirichlet Fields and other types of Number Fields.
Higher degree Harrison equivalence and Milnor -functor