Convergence Abscissas for Dirichlet Series with Multiplicative Coefficients

Abstract

This note deals with the relationship between the abscissas of simple, uniform and absolute convergence for the Dirichlet series $f(s)={\sum }_{n=1}^{\infty }{a}_n{n}^{-s}$, when the coefficients $a_n$ are either multiplicative or completely multiplicative.

Minor revision. Two new references added. This note has been accepted for publication in Expositiones Mathematicae

References in corpus (3)

• The Bohnenblust--Hille inequality for homogeneous polynomials is hypercontractive
• On the Sidon Constant for Dirichlet Polynomials
• An inequality of Hardy--Littlewood type for Dirichlet polynomials