On the Mean Values of the Dirichlet Series

Abstract

For Dirichlet series with arbitrary abscissa of absolute convergence, we investigate the relationhip between the increase in the maximum term and $\left( {\mathop \sum \nolimits_{n = 1}^\infty \left| {a_n } \right|^q \exp \{ q\sigma \lambda _n \} } \right)^{1/q}$ , q ∈ (0,+∞).