Eigenspaces of the ideal class group
The aim of this paper is to prove an analog of Gras’ conjecture for an abelian field and an odd prime dividing the degree assuming that the -part of group is cyclic.
Ein Satz über relativ-Galoissche Zahlkörper und seine Anwendang auf relativ-Abelsche Zahlkörper
Eine Klassenzahlformel für singuläre Moduln der Picardschen Modulgruppen
Ensembles de nombres algébriques et transformations rationnelles
Enumerating quartic dihedral extensions of with signatures
In a previous paper, we have given asymptotic formulas for the number of isomorphism classes of -extensions with discriminant up to a given bound, both when the signature of the extensions is or is not specified. We have also given very efficient exact formulas for this number when the signature is not specified. The aim of this paper is to give such exact formulas when the signature is specified. The problem is complicated by the fact that the ray class characters which appear are not all genus characters....
Errata to the papers : “Connections between for even quadratic Dirichlet characters ” and “Class numbers of appropriate imaginary quadratic fields, parts I and II”
Erratum “On the computation of quadratic -class groups”
Erratum to "Cohomology sets inside arithmetic groups" (Acta Arith. 107 (2003), 27-33)
Estimates of regulators and class numbers in function fields.
Étude d'un idéal particulier, d'indice fini dans le carré de l'idéal d'augmentation, associé à un caractère de Dirichlet d'un groupe fini
We describe here two sets of generators of an ideal , of finite index inside the square of the augmentation ideal of , associated to the Dirichlet character of the finite group . That peculiar ideal first appeared in questions related to the computation of class number formulas for abelian non ramified extensions of -fields cf. [2] and [3], satisfying certain special conditions which are outlined in the introduction of [1]. A rough idea of these formulas is given in §§2 and 6.
Examples of ...-invariants.
Explicit upper bounds for |L(1,χ)| for primitive even Dirichlet characters
Explicit upper bounds for the average order of and application to class number.
Exponent of class group of certain imaginary quadratic fields
Let be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form whose ideal class group has an element of order . This family gives a counterexample to a conjecture by H. Wada (1970) on the structure of ideal class groups.
Exponents of the class groups of complex quadratic fields