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
Fast computation of class fields given their norm group
Let be a number field containing, for some prime , the -th roots of unity. Let be a Kummer extension of degree of characterized by its modulus and its norm group. Let be the compositum of degree extensions of of conductor dividing . Using the vector-space structure of , we suggest a modification of the rnfkummer function of PARI/GP which brings the complexity of the computation of an equation of over from exponential to linear.
Finiteness of a class of Rabinowitsch polynomials
We prove that there are only finitely many positive integers such that there is some integer such that is 1 or a prime for all , thus solving a problem of Byeon and Stark.
Finitude de tours et -tours -ramifiées modérées, -décomposées
Soit un corps de nombres et soient et deux ensembles finis de places de ; on peut définir la tour de Hilbert de , -ramifiée modérée, -décomposée. Ceci permet d’obtenir, par exemple, la notion de tour de Hilbert au sens classique et de tour de Hilbert au sens restreint. On donne alors d’une part, un critère de finitude de cette nouvelle tour, critère construit à partir d’un résultat d’Odlyzko, puis d’autre part deux critères de non-finitude, le premier étant une conséquence d’un résultat...
Fitting ideals of class groups in a -extension
Formulae for the relative class number of an imaginary abelian field in the form of a product of determinants
Formules de classes pour les corps abéliens réels
Nous montrons des raffinements -adique et “caractères par caractères” de la formule d’indice de Sinnott pour un corps abélien totalement réel. De tels raffinements ont aussi été obtenus par Kuz’min avec des méthodes différentes (voir les commentaires en introduction). Nous donnons des applications à la théorie d’Iwasawa des unités semi- locales et cyclotomiques.
Fröhlich's and Chinburg's conjectures in the factorisability defect class group.