Dirichlet Series And Random Dirichlet Series In The Plane

This paper study the growth of Dirichlet series and random Dirichlet series in the plane. The full text is divided into two parts:1. Infinite order Dirichlet series in the half plane.2. Dirichlet series and random Dirichlet series in the whole plane.The first part of this article gives the definition of infinite order Dirichlet series, introduce the function U ( r )( r = 1x) followed type function obtained by Qinglai Xiong, study the growth of infinite order Dirichlet series on the half plane when the conditions weakened to (1.3) and obtain theorem 1.1 and theorem 1.2 ; In addition, the paper study the growth of the Dirichlet series and random Dirichlet series on the whole plane in the second part of this article, discuss the growth of the infinite Dirichlet series and random Dirichlet series in the weakened conditions, that is (2.3),we obtain the theorem 2.1, theorem 2.2, theorem 2.3 and theorem 2.4 in the text under this condition.