Abstract:

In this paper, the authors first study the growth and regular growth of Dirichlet series of finite order in the plane and  obtain two necessary and sufficient conditions; and then prove that the growth of random entire functions defined by random Dirichlet series of finite order in any horizontal
straight line is almost surely equal to the growth of entire functions defined by their corresponding Dirichlet series.

Key words: Dirichlet series, Random Dirichlet series, Type function, Proximate order, Growth