On Uniqueness Of Meromorphic Functions That Share Two Finite Sets

The uniqueness of mermorphic function will be cultivated by the master's thesis.This topic was prior proposed by Gross,and systemically developed by Yi Hongxun and Yang Chungchun's monograph of ((Uniqueness Theory of Meromorphic Functions)) of Chapter 10.There are a great comprehensive study of this area since then([2][3][4][5]).The bibliographies [6] [7] [8] [9][10] provide a further development.The thesis is self-contained.The Sectionl introduces Nevanlinna theory and define the uniqueness of mermorphic function of weight sharing finite set.In Section2.we discuss several lemmas,including uniqueness result regarding the mermorphic function which sharing one value,and some combinatoric results which play a crucial role in the following discussion.The Main body of this thesis is the construction of the sharing set which in section 3.In this section,we discuss two kinds of sets:respectively and establish the uniqueness results of the mermorphic counterpart.In Section 4,we deal with the results under the weaker assumption,and propose some further questions of this topics.