Inequalites for Dirichlet series with positive terms (Q949117)

The authors consider Dirichlet series of the form \[ \psi(s):=\sum_{n=1}^\infty \frac{a_{n}}{n^s} \] with \(s>1\) and \(a_{n}\) nonnegative for \(n\geq 1\), and they prove several general inequalities for such functions. Some inequalities involving the function \(Q(s):=\frac{\zeta'(s)}{\zeta(s)}- \frac{\psi'(s)}{\psi(s)}\), where \(s>1\) and \(\zeta(s)\) is the classical Riemann's zeta function, are also obtained.