Computing all elements of given index in sextic fields with a cubic subfield
Computing all monogeneous mixed dihedral quartic extensions of a quadratic field
Let be a given real quadratic field. We give a fast algorithm for determining all dihedral quartic fields with mixed signature having power integral bases and containing as a subfield. We also determine all generators of power integral bases in . Our algorithm combines a recent result of Kable [9] with the algorithm of Gaál, Pethö and Pohst [6], [7]. To illustrate the method we performed computations for
Computing Galois groups by means of Newton polygons
Computing higher rank primitive root densities
We extend the "character sum method" for the computation of densities in Artin primitive root problems given by Lenstra and the authors to the situation of radical extensions of arbitrary rank. Our algebraic set-up identifies the key parameters of the situation at hand, and obviates the lengthy analytic multiplicative number theory arguments that used to go into the computation of actual densities. It yields a conceptual interpretation of the formulas obtained, and enables us to extend their range...
Computing Iwasawa modules of real quadratic number fields
Computing special values of motivic -functions.
Concordant sequences and integral-valued entire functions
A classic theorem of Pólya shows that the function is the “smallest” integral-valued entire transcendental function. A variant due to Gel’fond applies to entire functions taking integral values on a geometric progression of integers, and Bézivin has given a generalization of both results. We give a sharp formulation of Bézivin’s result together with a further generalization.
Condition nécessaire et suffisante pour que certain groupe de Galois soit métacyclique
Soient est un entier sans facteurs carrés, , , le -corps de classes de Hilbert de , le -corps de classes de Hilbert de et le groupe de Galois de . Notre but est de montrer qu’il existe une forme de tel que le -groupe est non métacyclique et de donner une condition nécessaire et suffisante pour que le groupe soit métacyclique dans le cas où avec un nombre premier tel que .
Conditions globales pour les problèmes de plongement à noyau abélien
On considère un problème de plongement de corps de nombres algébriques, dont le noyau est abélien, et on suppose que les problèmes locaux correspondants sont résolubles. On montre que les conditions complémentaires de résolubilité, dites globales, sont fournies pour un nombre fini de représentations du noyau dans le groupe de classes d’idèles. Dans le cas d’un noyau cyclique, une seule suffit, et on la calcule.
Conditions under which is not generated by Dennis-Stein symbols
Congruence modules related to Eisenstein series
Congruence monoids
Congruence of Ankeny-Artin-Chowla type for cyclic fields
Congruence of Ankeny-Artin-Chowla type modulo p² for cyclic fields of prime degree l
Congruences among generalized Bernoulli numbers
Congruences dyadiques entre nombres de classes de corps quadratiques
Congruences Dyadiques entre nombres des classes de corps quadratiques.
Congruences et formes modulaires
Congruences modulo 16 for the class numbers of the quadratic fields Q(ñp) and Q(ñ2p) for p a prime congruent to 5 modulo 8
Congruences of Ankeny-Artin-Chowla type and the p-adic class number formula revisited
The purpose of this paper is to interpret the results of Jakubec and his collaborators on congruences of Ankeny-Artin-Chowla type for cyclic totally real fields as an elementary algebraic version of the p-adic class number formula modulo powers of p. We show how to generalize the previous results to congruences modulo arbitrary powers and to equalities in the p-adic completion of the field of rational numbers ℚ. Additional connections to the Gross-Koblitz formula and explicit congruences for...