The Normal Criteria Concerning Shared Values Of Meromorphic Function

In this thesis, we study normal criteria concerning shared values in the normal family theorem of meromorphic function. We get three normal criteria. The first one concerns the question that two functions share one complex number, in here, the func-tion form is the polynomial of the function multiply the n power of the k derivative of the function. The second one also concerns the question that two functions share one complex number, in here, the function form is that the k derivative of the function subtract the-n power of the function, the question in here is the relation between the k and the n, and the condition needed. The last one concerns one normal criterion have gotten by Lahiri and Dewan, here, we weaken their condition and get the result.This thesis consists of six chapters. The first chapter introduces the development process of the normal family, we focus on some historic results, at the same time, we introduce the development situation of the normal question that we concern. The second chapter introduces some definitions and theorems of the value distribution theorem, which are the basic knowledge in the complex analysis study. The third chapter introduces some definitions and theorems of the normal family, and the classic method that the elimination of the original value and Zalcman lemma in the proof of the normal criteria, and some normal criteria related to shared values. In the fourth and the fifth chapters we introduce the background and prove our results. In the last chapter, we give some open questions that concerning our results.