The Approximation And Type Of Finite Order Dirichlet Serieo

In this thesis, we make use of order and type of some basic knowledge of Dirichlet seriesto study lacunary generalized Dirichlet series of (p, q)(R)type, the approximation of finite orderDirichlet series in the whole plane, the approximation of generalized finite order Dirichlet series.The thesis is made up of four chapters.In the first chapter, we introduces a real index Dirichlet series and complex index Dirichletseries of the order and type of definitions and associated knowledge.In the second chapter, we study the relationship between the type TRof an entire functionrepresented by the generalized Dirichlet series of the finite order and the type TLin a horizontalline.In the third chapter, we mainly discuss the error in approximating Dirichlet series of finiteorder in the whole plane by Dirichlet polynomials is studied and some relation between the errorand the order, the proximate order and the type function of Dirichlet series is obtained.In the forth chapter, we mainly discuss the error in approximating the generalized Dirich-let series of finite order in the angle domain by the generalized Dirichlet polynomials is studiedand some relation between the error and the order, the proximate order and the type function ofDirichlet series is obtained.