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.