The Singular Direction And Argument Distribution Of Meromorphic Function

Content: in this thesis, we investigate some properties of value distribution of meromorphic functions by applying the theory and method of complex analysis.In chapter 1: we introduce some basic concept of the theory of the value distribution and some concept and notations which are used in the next chapters.In chapter 2: from researching the value distribution of meromorphic functions about the multiple value and the small functions in an angular domain, we prove an important inequality and investigate a singular direction of meromorphic functions with finite order about the multiple values and small functions by the important inequality.In chapter 3: on the basic of chapter 2, we further study the value distribution of meromorphic functions about the multiple values and the small functions in an angular domain and research the singular directions about the multiple values and small functions of the meromorphic functions of infinite order and prove the existence of the singular direction.In chapter 4: we research the theory of argument distribution of entire functions and meromorphic functions with iterated order combining its derivative, and generalize the known results.