Normal Families Of Meromorphic Functions Concerning Differential Polynomials And Shared Values

In 1920s,Nevanlinna studied meromorphic functions on the complex plane,and established the theory of value distribution of meromorphic functions named the Nevan-linna theory by the introduction of characteristic functions.The Nevanlinna theory not only laid a solid foundation to the study of meromorphic functions,but also made sig-nificant contributions to the classical function theory.Moreover,it also impacted the development of other branches of mathematics and other part on meromorphic func-tions.In this thesis,we mainly review the relevant theories of value distribution of meromorphic functions,and proved two new normality criteria of families of meromor-phic functions concerning the differential polynomials[L（f）]^（k）and[L（g）]^（k）sharing value and sharing functions.This thesis is divided into four chapters:The first chapter is introduction.In this part,we simply introduce the history and current situation of the distribution theory.The second chapter introduces the basic knowledge on value distribution theory and normal theory and some of famous normal theory.The third chapter is our main results and their proofs.From the research of Hay-man theory,which related functions and its derivative,by considering the uniqueness theorems of meromorphic functions about sharing values,using the knowledge of theo-ry of value distribution,what extend the meromorphic functions f,g to their differential polynomials[L（f）]^（k）and[L（g）]^（k）sharing values and sharing holomorphic functions.The last chapter is conclusion.Further analysis and explanation of related value distribution theory and new types of normality criteria combining with our results are proposed.