On the Stability of the Maximum Term of the Entire Dirichlet Series

Abstract

We establish necessary and sufficient conditions for the logarithms of the maximum terms of the entire Dirichlet series \(F(z) = \sum\nolimits_{n = 0}^{ + \infty } {a_n e^{z\lambda _n } }\) and \(B(z) = \sum\nolimits_{n = 0}^{ + \infty } {a_n b_n e^{z\lambda _n } }\) to be asymptotically equivalent as Re z → +∞ outside a certain set of finite measure.