Growth of Random Dirichlet Series of Zero Order in Plane

The growth of zero order random Dirichlet series in the plane was studied.When random variables series {Xn(ω)} satisfies the certain condition,some results about their growth are obtained from the study.These results show that the growth of entire function determined by the zero order random Dirichlet series is almost the same with corresponding growth of random Dirichlet series in any horizontal straight lines.