Uniqueness Of Meromorphic Functions And Their Differential Polynomials

In 1925,the famous Finnish mathematician R.Nevanlinna introduced the characteristic functions of meromorphic functions and gave the famous Nevanlinna theory.For over a half century,many foreign and domestic mathematicians such as: F.Gross,W.K.Hayman,Q.L.Xiong,H.X.Yi,C.C.Yang,et al.have devoted themselves to the research and obtained lots of elegant results on the research of the uniqueness theory.This thesis is mainly discussed the uniqueness of meromorphic functions whose derivatives sharing different sets,and studied the uniqueness of meromorphic functions concerning differential polynomials.The main structure of the thesis is organized as follows:In section one,we mainly introduce the basic Nevanlinna theory and some classical theory of the uniqueness results.In section two,we are mainly devoted to the uniqueness of meromorphic functions whose 6)-th derivatives sharing different sets.Moreover,we prove the uniqueness theorems for meromorphic functions whose 6)-th derivatives sharing different sets CM or IM,which generalize the results of Yi and Lin.In section three,we study the uniqueness of meromorphic functions concerning differential polynomials,and obtain the uniqueness theorems that the different differential polynomials of meromorphic functions share one value,which improve some former results given by Lin,Yi and Zhang.In section four,we mainly present some problems related to our results.