Normality Of Meromorphic Functions Related To Zero And Differential Polynomials

The normal families theory of meromorphic functions has been developed for a long time.It not only has important theoretical significance,but also has rich practical application value.As one of the important directions in the field of complex analysis,many mathematicians at home and abroad have made great contributions in this area and have obtained many famous achievements.This dis-sertation mainly discusses the normal families of meromorphic functions involving the number of zeros and differential polynomials,and obtains three related normal criterion.It mainly includes the following six chapters.The first chapter mainly introduces the background and meaning of normal families of meromorphic functions,and the development of the problems involved in this paper.The second chapter briefly introduces some definitions and theorems of the value distribution theorem,and gives some common symbols and basic results.The third chapter explains some concepts and basic theorems of the normal families,and the method of proof of the normal criterion.In the fourth chapter,we consider to generalize f^k?z?-1 to (f^k?z?)^q-1,and obtain the normality of families of meromorphic functions associated with zeros.An example is given to illustrate the necessity of limiting the number of zeros in the theorem.In the fifth chapter,we study the normality of families of meromorphic func-tions concerning differential polynomials,which generalizes the result of Chang Jianming.In the sixth chapter,we mainly discuss the normality of families of meromor-phic functions related to shared values.We strengthen the conditions in the exiting results to f?z??0,and eliminate the pole multiplicity limits,which generalizes the result of Shang Hua.