The Growth Of Dirichlet Series And Random Dirichlet Series Of Finite Order

This paper deals with the growth of Dirichlet series and random Dirichlet series of finiteorder in the two cases:1. The Dirichlet series of finite order in the right half-plane.2.The Dirichlet series and random Dirichlet series of finite order in the whole plane.The first part outlines the history of the researches on Dirichlet series and randomDirichlet series, combines with the current situation of the development and presents resultsobtained in the paper.The second part presents Knopp-Kojima method, under the conditionσ_u=0,Deals with the the growth of Dirichlet series of finite order in the right half-plane, andobtains Theorem2.1and Theorem2.2.In the section1of Chapter3, under the conditionσ_a=-∞,Deals with the the growth of Dirichlet series of finite order in the whole plane, and obtainsTheorem3.1and Theorem3.2. In the section2of Chapter3disscusses the growth of randomDirichlet series of finite order in the whole plane, and obtains Theorem3.3and Theorem3.4.