Meromorphic Functions Concerning Shared Sets

In1925, R.Nevanlinna established two fundamental theorems which started the modern researches of value distribution for meromorphic functions, and proved the famous five-value theorem and four-value theorem, which opened up the research on the uniqueness of meromorphic functions. Since then, many mathematicians have focused on the uniqueness of meromorphic functions that share four values (three values, two values or even one value, and the more general, some sets) under some additional conditions. It is well known that there have been many excellent results and the uniqueness theory of meromorphic functions has highly developed in recent decades. Especially, F. Gross in1976posed the problems on the uniqueness sets of meromorphic functions and the minimum cardinality of shared sets. Afterwards, the research on meromorphic functions concerning shared sets seems to be a very hot subject. In the thesis, we shall use the method of weighted sharing and pseudo sharing to study the uniqueness of meromorphic functions sharing two sets or three sets.This thesis is divided into four sections:In section one, we mainly introduce the basic Nevanlinna theory and some classical uniqueness theory.In section two, we use the method of weighted sharing to discuss the uniqueness problems on meromorphic functions sharing two sets, which generalize the results of Yi and Li, Yang and so on.In section three, we are mainly concerned with the uniqueness of meromorphic functions sharing three sets with weighted sharing and pseudo sharing. Our theorems improve some former results given by Lin, Yi and so on.In section four, we mainly present some problems related to our results.