The Uniqueness Of Meromorphic Functions Sharing Small Functions IM

The analytical functions in complex plane C are called entire functions, and the functions which are analytical except on the poles in complex plane are called meromorphic functions.The uniqueness theory of meromorphic functions mainly studies conditions under which there exists essentially only one function satisfying these conditions.Mues founded a lemma concerning two meromorphic functions that share four distinct IM value, which is widely applied.My classmate Zhou Zijiong has generalized the Mues lemma to the small functions case. I have participated in part of his work, too.The main part of my paper is to generalize one of Reinders'theorem, using the generalization of Mues lemma. In this prove, we construct some assistant functions, also hoping that they will be helpful in the future.