Uniqueness Of Meromorphic Functions Sharing One Common Value

In 1920s, R. Nevanlinna introduced the characteristic functions of meromorphic functions and gave the famous Nevanlinna theory which is one of the greatest achievements in mathematics in the 20th century. This theory is considered to be the basis of modern meromorphic function theory, and it has a very important effect on the development and syncretic of many mathematical branches. Especially, Nevanlinna theory has been used as a very powerful tool and has made the research field mo(?)e active and popular after it was successfully applied to the research of the global analytic solutions of complex differential equations. Taking advantage of the theory just made by himself, R. Nevanlinna studied the conditions with which a meromorphic function can be determined and obtained two celebrated uniqueness theorems on meromorphic functions, which are called Nevanlinna's five-value theorem and four-value theorem. Since then, the research of meromorphic functions began. For over a half century, many foreign and domestic mathematicians have devoted themselves to the research and obtained lots of elegant results on the research of the uniqueness theory. In the past two decades, Professo(?) Yi Hongxun did much creative work on the uniqueness theory of meromo(?)phic functions, and well improved the development of the uniqueness theory. In this paper,we will give some results on the uniqueness of memomorphic functions sharing one common value IM under the guidance of Professor Yi Hongxun. This thesis consists of three chapters.In chapter 1, we will briefly introduce some fundamental results, definitions and some notations.In chapter 2, we study the uniqueness theorems of meromorphic functions...