On the abscissas of convergence of Dirichlet series

Abstract

For the Dirichlet series of the form $F(z,\omega )={\sum }_{k=0}^{+\infty }{f}_k(\omega )e^{z{\lambda }_k(\omega )}$ $(z\in \mathbb{C},$ $\omega \in \Omega )$ with pairwise independent real exponents $({\lambda }_k(\omega ))$ on probability space $(\Omega ,\mathcal{A},P)$ an estimates of abscissas convergence and absolutely convergence are established.