The Growth Of Dirichlet Series And Random Dirichlet Series On The Plane

This paper studies the growth of Dirichlet series and random Dirichlet series in the plane. The full text is divided into two parts :1. Zero order Dirichlet series in the whole plane.2. Dirichlet series and random Dirichlet series in the half PlaneThe first part of this article introduce the function U( x ) (x = e~σ) followed type function obtained by Qinglai xiong, and gives the Dirichlet series the informal definition of normal growth, Study the growth of zero-order Dirichlet series in the the whole plane and obtain a necessary and sufficient condition on the zero- order Dirichlet series ,that is Theorem 1.1 and theorem 1.2 in the text; In addition, The paper study the growth of of the Dirichlet series and random Dirichlet series on the right half-plane in the second part of this article , and obtain a necessary and sufficient conditions on the growth of zero-order Dirichlet series by introducing the Indicator ; we also study the growth of the finite-and infinite - Dirichlet series and random Dirichlet series in the weakened conditions, that is (0 <ρ<+∞)we obtain the Theorem 2.3, theorem 2.4 and theorem 2.5 in the text under this condition.