Approximate formulae for L(1,χ), II
Approximations to -logarithms and -dilogarithms, with applications to -zeta values.
Approximative Funktionalgleichungen und Mittelwertsätze für Dirichletreihen, die Spitzenformen assoziiert sind.
ARI/GARI, la dimorphie et l'arithmétique des multizêtas : un premier bilan
Nous tentons, dans ce survol, de présenter une structure méconnue : l'algèbre de Lie ARI et son groupe GARI. Puis nous montrons quels progrès elle a déjà permis de réaliser dans l'étude arithmético-algébrique des valeurs zêta multiples et aussi quelles possibilités elle ouvre pour l'exploration du phénomène plus général de /emph{dimorphie numérique}.
Arithmetic of linear forms involving odd zeta values
A general hypergeometric construction of linear forms in (odd) zeta values is presented. The construction allows to recover the records of Rhin and Viola for the irrationality measures of and , as well as to explain Rivoal’s recent result on infiniteness of irrational numbers in the set of odd zeta values, and to prove that at least one of the four numbers , , , and is irrational.
Arithmetic Subseries of Series with Multiplicative Terms
Arithmetical functions with periodic zeros
Arithmetical properties of finite rings and algebras, and analytic number theory. IV. Relative asymptotic enumeration and L-series.
Arithmetical Tauberian theorems
Artin formalism and heat kernels.
Artin formalism for Selberg zeta functions of co-finite Kleinian groups
Let be a finite-volume quotient of the upper-half space, where is a discrete subgroup. To a finite dimensional unitary representation of one associates the Selberg zeta function . In this paper we prove the Artin formalism for the Selberg zeta function. Namely, if is a finite index group extension of in , and is the induced representation, then . In the second part of the paper we prove by a direct method the analogous identity for the scattering function, namely , for an appropriate...
Artin's conjecture in algebraic number fields and a related question concerning units
Artin's conjecture, Turing's method, and the Riemann hypothesis.
Aspectos computacionales de los números primos (I).
Asymptotic analysis and special values of generalised multiple zeta functions
This is an expository article, based on the talk with the same title, given at the 2011 FASDE II Conference in Będlewo, Poland. In the introduction we define Multiple Zeta Values and certain historical remarks are given. Then we present several results on Multiple Zeta Values and, in particular, we introduce certain meromorphic differential equations associated to their generating function. Finally, we make some conclusive remarks on generalisations of Multiple Zeta Values as well as the meromorphic...
Asymptotic Behavior of Some Power Series with ...-functions in the Coefficients.
Asymptotic Estimates on Finite Abelian Groups
Asymptotic expansions of certain q-series and a formula of Ramanujan for specific values of the Riemann zeta function
Asymptotic expansions of the mean values of Dirichlet L-functions III.
Asymptotic expansions of the mean values of Dirichlet L-functions.