Uniqueness Theory Of Meromorphic Functions Of One Or Several Complex Variables

The value distribution theory of meromorphic functions founded by R. Nevanlinna, a famous Finnish mathematician, is surely one of the most important 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 syncretism of many mathematical branches. Especially, the Nevanlinna theory supplies a very powerful tool to the research of the global analytic solutions of complex differential equations and also makes the research field more active and popular after it was successfully applied to get insight into the solutions of complex differential equations. With the development of the Nevanlinna theory itself, some new mathematical branches with it as their principal tool have appeared. In the late 1920s, R. Nevanlinna^[1] studied the conditions with which a meromorphic function can be determined by the theory just established by himself, and obtained three celebrated uniqueness theorems for meromorphic functions, which are usually called Nevanlinna's five-value theorem and Nevanlinna's four-value theorem and Nevanlinna's three-value theorem. This launched the investigation of uniqueness theory of meromorphic functions and in particular the shared values of meromorphic functions.In the past half a century, in Japan, China, Germany, England, the former Soviet Union and the United States, many mathematicians denoted themselves to the research into the uniqueness theory of meromorphic functions, and thus it became an important branch in the complex analysis field, even up till now, which is still active.The present dissertation is part of the author's research work on the uniqueness problem of meromorphic functions over C that share values with the linear combination of their...