Computing Igusa's local zeta functions of univariate polynomials, and linear feedback shift registers.
Computing -removed -orderings and -orderings of order
We develop a recursive method for computing the -removed -orderings and -orderings of order the characteristic sequences associated to these and limits associated to these sequences for subsets of a Dedekind domain This method is applied to compute these objects for and .
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.
Congruences de coefficients de séries de Taylor (Application aux nombres de Bernoulli-Hurwitz)
Congruences entre séries d'Eisenstein, dans le cas supersingulier.
Congruences modulo between factors for cuspidal representations of
Let be two different prime numbers, let be a local non archimedean field of residual characteristic , and let be an algebraic closure of the field of -adic numbers , the ring of integers of , the residual field of . We proved the existence and the unicity of a Langlands local correspondence over for all , compatible with the reduction modulo in [V5], without using and factors of pairs. We conjecture that the Langlands local correspondence over respects congruences modulo between...
Congruences pour les nombres de Schröder
Conjugacy classes of series in positive characteristic and Witt vectors.
Let be the algebraic closure of and be the local field of formal power series with coefficients in . The aim of this paper is the description of the set of conjugacy classes of series of order for the composition law. This work is concerned with the formal power series with coefficients in a field of characteristic which are invertible and of finite order for the composition law. In order to investigate Oort’s conjecture, I give a description of conjugacy classes of series by means...
Constructing class fields over local fields
Let be a -adic field. We give an explicit characterization of the abelian extensions of of degree by relating the coefficients of the generating polynomials of extensions of degree to the exponents of generators of the norm group . This is applied in an algorithm for the construction of class fields of degree , which yields an algorithm for the computation of class fields in general.
Construction des extensions primitives d’un corps -adique
Continuous Cohomology and p-Adic Galois Representations.
Continuous functions on compact subsets of local fields
Convolution de Rankin p-adique.
Corps de fonctions algébriques
Correction to "Computing Galois groups by means of Newton polygons" (Acta Arith. 115 (2004), 71-84)
Correction to the paper "Explicit form of the modular equation".
Correspondance de Langlands locale pour et conducteurs de paires
Counting colorings on varieties.
We present a combinatorial mechanism for counting certain objects associated to a variety over a finite field. The basic example is that of counting conjugacy classes of the general linear group. We discuss how the method applies to counting these and also to counting unipotent matrices and pairs of commuting matrices.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].
Counting periodic points of -adic power series
Courbes définies sur les corps de séries formelles et loi de réciprocité (Acta Arithmetica 42 (1982), p. 101-106) (Errata)