The Growtrh Of Dirichlet Series And Random Dirichlet Series

This paper deals with the growth of Dirichlet series and random Dirichlet series in the two aspects:1. The Proximate Zero Order ( R )of Dirichlet Series and random Dirichlet Series in the right half-plane.2. Deficient functions of random Dirichlet series of infinite Order.The first chapter has weakened the condition of the growth and regular growth of the proximate zero order ( R ) of the analytic Dirichlet series which was proposed by the predecessors, and obtains a better result, and obtains when the random variable sequence satisfies the certain condition, in the right half-plane, growth of a proximate zero order ( R ) of random analytic function which is determined by the random Dirichlet series is almost surely same with corresponding proximate zero order ( R ) of random Dirichlet series in any right half straight line.The second chapter studies deficient function of the infinite order random Dirichlet series, and obtains that the infinite order random Dirichlet series do not have almost surely arbitrary finite order deficient function in the whole plane and in the right half-plane.