The Growth Of B-valued Dirichlet Series And The Laplace-Stieltjes Type Integral

In this thesis, we make use of order and type of some basic knowledge of Dirichlet series and the principles and methods of Dirichlet series to study the (p,q)-(R) order and (p,q)-(R) type of a Laplace-Stieltjes type integral, the growth of B-valued Dirichlet series of finite order in the plane and the growth of the B-valued generalized Dirichlet series. The thesis is made up of four chapters.In the first chapter, we introduce the background of Dirichlet series and associated knowledge.In the second chapter, we mainly study some relationships between the maximum modulus and the maximum terms, the An and the wn(n=1,2,...) of the Laplace-Stieltjes type integral, some theorems on estimating the (p,q)-(R) order and the (p,q)-(R) type are obtained.In the third chapter, we study some relationships between the growth of B-valued Dirichlet series of finite order in the plane and coefficients.In the forth chapter, we mainly discuss the growth of the B-valued generalized Dirichlet series in the angle domain.