Fundamental solutions of pseudo-differential operators over -adic fields
Holomorphy of local zeta functions for curves.
Idele characters in spectral synthesis on
Let , . We construct Dirichlet series where for each fixed in a half plane, , as a function of , is a non-synthesizable absolutely convergent Fourier series. Because of the way the frequencies in are chosen, we are motivated to introduce a class of synthesizable absolutely convergent Fourier series which are defined in terms of idele characters. We solve the “problem of analytic continuation” in this setting by constructing pseudo-measures, determined by idele characters, when .
Intégration -adique, selon A. Volkenborn
Interpolation p-adique des dérivées logarithmiques et fonctions L p-adiques associées à des courbes elliptiques à multiplication complexe.
Introduction aux travaux de Dwork
Iwasawa-theory of abelian varieties at primes of non-ordinary reduction.
Kida's formula and congruences.
Kummer congruences for expressions involving generalized Bernoulli polynomials
We illustrate how a particular expression, involving the generalized Bernoulli polynomials, satisfies systems of congruence relations if and only if a similar expression, involving the generalized Bernoulli numbers, satisfies the same congruence relations. These congruence relations include the Kummer congruences, and recent extensions of the Kummer congruences provided by Gunaratne.
Kummer congruences for values of Bernoulli and Euler polynomials
Kummer's calculation of Lp (1,...).
Le prolongement -adique analytique des fonctions de Rankin
Le système d’Euler de Kato
Ce texte est consacré au système d’Euler de Kato, construit à partir des unités modulaires, et à son image par l’application exponentielle duale (loi de réciprocité explicite de Kato). La présentation que nous en donnons est sensiblement différente de la présentation originelle de Kato.
Les fonctions -adiques de Dirichlet
Li coefficients for automorphic -functions
Xian-Jin Li gave a criterion for the Riemann hypothesis in terms of the positivity of a set of coefficients
Local -characters in torsion rings
Let be a rational prime and a complete discrete valuation field with residue field of positive characteristic . When is finite, generalizing the theory of Deligne [1], we construct in [10] and [11] a theory of local -constants for representations, over a complete local ring with an algebraically closed residue field of characteristic , of the Weil group of . In this paper, we generalize the results in [10] and [11] to the case where is an arbitrary perfect field.
Logarithmic derivatives of Dirichlet -functions and the periods of abelian varieties
Majoration du nombre de zéros dans un disque des fonctions -adiques
Nombre de points des variétés de Shimura sur un corps fini
Nombres de Bernoulli et fonctions -adiques