Kida's formula and congruences.
Le problème de Lehmer relatif en dimension supérieure
Nous généralisons en dimension supérieure un théorème d’Amoroso et Zannier concernant le problème de Lehmer relatif. Nous minorons la hauteur d’un point d’un tore en fonction de son indice d’obstruction sur , l’extension abélienne maximale de , à condition qu’il ne soit pas contenu dans une sous-variété de torsion de petit degré. Nous en déduisons une minoration du minimum essentiel d’une sous-variété non contenue dans un sous-groupe algébrique propre en fonction de son indice d’obstruction sur...
Lois de reciprocite primitives.
Lower bounds for relative class numbers of imaginary abelian number fields and CM-fields
Majoration au point 1 des fonctions L associées aux caractères de Dirichlet primitifs, ou au caractère d'une extension quadratique d'un corps quadratique imaginaire principal.
Maximal independent systems of units in global function fields
Maximal unramified extensions of imaginary quadratic number fields of small conductors, II
In the previous paper [15], we determined the structure of the Galois groups of the maximal unramified extensions of imaginary quadratic number fields of conductors under the Generalized Riemann Hypothesis (GRH) except for 23 fields (these are of conductors ) and give a table of . We update the table (under GRH). For 19 exceptional fields of them, we determine . In particular, for , we obtain , the fourth Hilbert class field of . This is the first example of a number field whose...
Minoration au point 1 des fonctions L et détermination des corps sextiques abéliens totalement imaginaires principaux
Modèle de Legendre d'une courbe elliptique à multiplication complexe et monogénéite d'anneaux d'entiers II
Modèle de Legendre d'une courbe elliptique à multiplication complexe et monogénéité d'anneaux d'entiers. I
Module structure of integers in metacyclic extensions
Monographic study of a cubic field.
Nombre de -classes invariantes. Application aux classes des corps abéliens
Nombre d'extensions abéliennes sur Q
The aim of this paper is to give the numbers of abelian number fields with given degree and ramification indices. We describe, also, an algorithm to compute all these fields.
Non-existence and splitting theorems for normal integral bases
We establish new conditions that prevent the existence of (weak) normal integral bases in tame Galois extensions of number fields. This leads to the following result: under appropriate technical hypotheses, the existence of a normal integral basis in the upper layer of an abelian tower forces the tower to be split in a very strong sense.
Normal integral bases for Emma Lehmer’s parametric family of cyclic quintics
Explicit normal integral bases are given for some cyclic quintic fields defined by Emma Lehmer’s parametric family of quintics.
Note on the congruence of Ankeny-Artin-Chowla type modulo p²
The results of [2] on the congruence of Ankeny-Artin-Chowla type modulo p² for real subfields of of a prime degree l is simplified. This is done on the basis of a congruence for the Gauss period (Theorem 1). The results are applied for the quadratic field ℚ(√p), p ≡ 5 (mod 8) (Corollary 1).
Note on the Hilbert 2-class field tower
Let be a number field with a 2-class group isomorphic to the Klein four-group. The aim of this paper is to give a characterization of capitulation types using group properties. Furthermore, as applications, we determine the structure of the second 2-class groups of some special Dirichlet fields , which leads to a correction of some parts in the main results of A. Azizi and A. Zekhini (2020).
On a conjecture concerning minus parts in the style of Gross
On a construction on p-units in abelian fields.