Distributions homogènes sur une algèbre de Jordan
Doubles mélanges des polylogarithmes multiples aux racines de l’unité
Enumerating non-equivalent matrices over principal ideal domains
Equations for Mahler measure and isogenies
We study some functional equations between Mahler measures of genus-one curves in terms of isogenies between the curves. These equations have the potential to establish relationships between Mahler measure and especial values of -functions. These notes are based on a talk that the author gave at the “Cuartas Jornadas de Teoría de Números”, Bilbao, 2011.
Ergodic Universality Theorems for the Riemann Zeta-Function and other -Functions
We prove a new type of universality theorem for the Riemann zeta-function and other -functions (which are universal in the sense of Voronin’s theorem). In contrast to previous universality theorems for the zeta-function or its various generalizations, here the approximating shifts are taken from the orbit of an ergodic transformation on the real line.
Errata to “The Dirichlet series of : On an error term associated with its coefficients” (Acta Arith. 75 (1996), 39-69)
Errata to the paper "On a functional equation satisfied by certain Dirichlet series" (Acta Arith. 71 (1995), 265-272)
Erratum - Zeta functions for the Riemann zeros
Euler numbers and polynomials associated with zeta functions.
Evaluations of -fold Euler/Zagier sums: a compendium of results for arbitrary .
Evaluations of some variant Euler sums.
Existence of a non-entire twist for a class of L-functions
Extension of analytic number theory and the theory of regularized harmonic series from Dirichlet series to Bessel series.
Extension of Estermann’s theorem to Euler products associated to a multivariate polynomial
Given a multivariate polynomial with integral coefficients verifying an hypothesis of analytic regularity (and satisfying ), we determine the maximal domain of meromorphy of the Euler product and the natural boundary is precisely described when it exists. In this way we extend a well known result for one variable polynomials due to Estermann from 1928. As an application, we calculate the natural boundary of the multivariate Euler products associated to a family of toric varieties.
Factorization of constants involved in conjectural moments of zeta-functions.
Familles de fonctions de formes automorphes et applications
Une notion importante qui a émergé de la théorie analytique des fonctions ces dernières années, est celle de famille. Par exemple les familles de fonctions interviennent naturellement dans le modèle probabiliste des matrices aléatoires de Katz/Sarnak qui vise à prédire la répartition des zéros des fonctions . L’analyse des fonctions en famille intervient également dans la résolution (inconditionnelle) de divers problèmes ayant une signification arithmétique profonde, tel que le problème de...
Flows of Mellin transforms with periodic integrator
We study Mellin transforms for which is periodic with period in order to investigate ‘flows’ of such functions to Riemann’s and the possibility of proving the Riemann Hypothesis with such an approach. We show that, excepting the trivial case where , the supremum of the real parts of the zeros of any such function is at least .We investigate a particular flow of such functions which converges locally uniformly to as , and show that they exhibit features similar to . For example, ...
Fonction L des courbes modulaires
Fonctions zêta des hauteurs
Ce papier présente les récents progrès concernant les fonctions zêta des hauteurs associées à la conjecture de Manin. En particulier, des exemples où on peut prouver un prolongement méromorphe de ces fonctions sont détaillés.
Fractions de Bernoulli-Carlitz et opérateurs -Zeta
On introduit une déformation des séries de Dirichlet d’une variable complexe , sous la forme d’un opérateur pour chaque nombre complexe , agissant sur les séries formelles sans terme constant en une variable . On montre que les fractions de Bernoulli-Carlitz sont les images de certains polynômes en par les opérateurs associés à la fonction de Riemann aux entiers négatifs.