Low moments of Dirichlet series
Published in Acta Mathematica Hungarica
We determine the maximum possible size of the qth moment of a Dirichlet series, for 1 ≦ q≦ 2.
Asymptotic expansions for linear homogeneous divide-and-conquer recurrences: Algebraic and analytic approaches collated
Among all sequences that satisfy a divide-and-conquer recurrence, those which are rational with respect to a numeration system are certainly the most basic and the most essential. Nevertheless, until recently this specific class of sequences has not been systematically studied from the asymptotic standpoint. We recall how a mechanical process desig...
Isometric and invertible composition operators on weighted Bergman spaces of Dirichlet series
We show that a composition operator on weighted Bergman spaces $\mathcal{A}_{\mu}^p$ is invertible if and only if it is Fredholm if and only if it is an isometry.
Composition operators on weighted Bergman spaces of Dirichlet series
We study boundedness and compactness of composition operators on weighted Bergman spaces of Dirichlet series. Particularly, we obtain in some speci c cases, upper and lower bounds of the essential norm of these operators and a criterion of compactness on classicals weighted Bergman spaces. Moreover, a su cient condition of compactness is obtained u...
On complete monotonicity of the Riemann zeta function
Published in Journal of Inequalities and Applications
Under the assumption of the Riemann hypothesis for the Riemann zeta function and some Dirichlet L-series we demonstrate that certain products of the corresponding zeta functions are completely monotonic. This may provide a method to disprove a certain Riemann hypothesis numerically. MSC:30E15, 33D45.
Accurate approximations of concrete creep compliance functions based on continuous retardation spectra
Published in Computers and Structures
This paper presents a detailed analysis of the continuous retardation spectra corresponding to a number of concrete creep models stipulated by various codes and recommendations. Approximations of various orders based on the Post–Widder formula are constructed, and the accuracy of the corresponding Dirichlet series approximating the compliance funct...
Extending a characterization of majorization to infinite dimensions
Published in Linear Algebra and Its Applications
We consider recent work linking majorization and trumping, two partial orders that have proven useful with respect to the entanglement transformation problem in quantum information, with general Dirichlet polynomials, Mellin transforms, and completely monotone sequences. We extend a basic majorization result to the more physically realistic infinit...
Mean Values of Certain Multiplicative Functions and Artin's Conjecture on Primitive Roots
We discuss how one could study asymptotics of cyclotomic quantities via the mean values of certain multiplicative functions and their Dirichlet series using a theorem of Delange. We show how this could provide a new approach to Artin's conjecture on primitive roots. We focus on whether a fixed prime has a certain order modulo infinitely many other ...
Mean Values of Certain Multiplicative Functions and Artin's Conjecture on Primitive Roots
We discuss how one could study asymptotics of cyclotomic quantities via the mean values of certain multiplicative functions and their Dirichlet series using a theorem of Delange. We show how this could provide a new approach to Artin's conjecture on primitive roots. We focus on whether a fixed prime has a certain order modulo infinitely many other ...
The Cardon and Robert Criterion for the Riemann hypothesis
Published in Analysis
In this paper, we give a reformulation of the Riemann hypothesis for automorphic L-functions in terms of orthogonal polynomials which extends the Cardon and Roberts criterion for the classical case of the Riemann zeta function. Actually, for any principal L-function L(s, π) attached to irreducible cuspidal unitary automorphic representation π of GL...
