We consider various Hilbert spaces of Dirichlet series whose norms are given by weighted l2 norms of the Dirichlet coefficients. We characterize the multiplier algebras for some of these spaces. 0 Introduction Let w = {wn}n=n0 be a sequence of positive numbers. In this paper we are concerned with Hilbert spaces of functions representable by Dirichlet series: H w = {

We consider a class of Dirichlet series which is more general than the Selberg class. Dirichlet series in this class, have meromorphic continuation to the whole plane and satisfy a certain functional equation. We prove, under the assumption of a certain hypothesis concerning the density of zeros on average, that the sequence formed by the imaginary parts of the zeros of a Dirichlet series in th...

1 The classical Möbius function 1.1 Arithmetic functions and Dirichlet series. Write N (meant to encode some arithmetic feature of each number n). To each arithmetic function f one associates a Dirichlet series F (s) = n≥1 f (n) n s thought of as a function defined on some open set of the complex plane. Analytic number theory is to a large extent the study of arithmetic functions in terms of th...