The Approximation And Growth Of Dirichlet Of Series In The Whole Plane

Based on the investigation of dirichlet serise with real exponents, in this thesis we mainly study the existence of entire functions represented by dirichlet series using the classical theory and method of entire functions and dirichlet series. The thesis is made up of four chapters.In the first chapter, we introduce Dirichlet series of the order and type of definitions and associated knowledge.In the second chapter, generalized order and type of Dirichlet series in the whole plane are given, we investigate the error En₁?f,?? in approximating Dirichlet series of generalized order and type in the whole plane. We also get some results of remainder Rn?f,?? in the half plane.In the third chapter, by the method of Knopp-Kojima, we define the maximum modulus, the maximum term, and study the regular order of the slow growth of Dirichlet series on the whole plane. Some interesting relations of the regular order of growth of Dirichlet series are obtained. In addition, we introduce the type function, and study the regular of the growth of the type function.In the four chapter, by the method of Knopp-Kojima, we introduce a new class of function, and define the ? - order of the slow growth of Dirichlet series on the whole plane. Some interesting relations between on the maximum modulus, the maximum term and ? - order of Dirichlet series are obtained. In addition, we introduce the type function, and study the approximation and growth of the type function.