Study On Value Distribution And Uniqueness Of Meromorphic Functions

In this paper,we focus on the quasi-deficient value problem of transcendental meromorphic functions and the uniqueness of meromorphic functions in value distribution theory.The full text mainly includes the following parts:In chapter 1,the value distribution theory of meromorphic functions and the research progress of uniqueness are described.In chapter 2,the basic knowledge of value distribution theory and some important concepts are briefly introduced.In chapter 3,we mainly study the problem of Valiron quasi-degenerate value over the transcendental meromorphic functions and prove that:Let f(z)be a transcendental meromorphic function such that(?),then there exist a(?),such that the set is a subset ofwheres(?),which is a set of finitem-measure.In chapter 4,we study the uniqueness of meromorphic functions that share two small functions with their derivatives.We prove the following result:Let f be a nonconstant meromorphic function such that(?),and let a,b be two distinct small functions of f with (?)and (?).If f and (?)share a and b IM,then(?).In chapter 5,this paper summarizes and points out the further conjecture on the basis of this paper.