Sur les corps quadratiques imaginaires dont le 3-rang du groupe des classes est supérieur à 1
Valeurs minima du discriminant pour certains types de corps de degré 7
Parmi les corps de nombres de degré 7 ayant 3 places réelles six seulement, à isomorphisme près, ont un discriminant plus petit que 678876. Tous ces corps sont euclidiens et ont été découverts par Leutbecher et Martinet (Astérisque, 94 (1982)), 87–131. Dans une seconde partie on montre comment l’acceptation de l’hypothèse de Riemann généralisée permet de trouver les 10 premiers minima de la valeur absolue du discriminant pour les corps de degré 7 ayant 1 place réelle et les 20 premiers minima du...
A polynomial reduction algorithm
The algorithm described in this paper is a practical approach to the problem of giving, for each number field a polynomial, as canonical as possible, a root of which is a primitive element of the extension . Our algorithm uses the algorithm to find a basis of minimal vectors for the lattice of determined by the integers of under the canonical map.
Category with a natural cone
Generally, in homotopy theory a cylinder object (or, its dual, a path object) is used to define homotopy between morphisms, and a cone object is used to build exact sequences of homotopy groups. Here, an axiomatic theory based on a cone functor is given. Suspension objects are associated to based objects and cofibrations, obtaining homotopy groups referred to an object and relative to a cofibration, respectively. Exact sequences of these groups are built. Algebraic and particular examples are given....
Counting discriminants of number fields
For each transitive permutation group on letters with , we give without proof results, conjectures, and numerical computations on discriminants of number fields of degree over such that the Galois group of the Galois closure of is isomorphic to .
Counting cyclic quartic extensions of a number field
In this paper, we give asymptotic formulas for the number of cyclic quartic extensions of a number field.
A new algorithm for the computation of logarithmic -class groups of number fields.
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