Shared Values And Normal Families

Twenties of the twentieth century, the introduction of the Finnish mathematician R. Nevanlinna characteristic function of meromorphic functions, Nevanlinna theory as established, as the twentieth century one of the greatest achievements in math. It not only established the modern basis of the theory of meromorphic functions, and on many other branches of mathematics and the integration of the cross had a significant impact.Since the introduction of P. Montel since the concept of normal families, normal family theory has made great progress, there are three stages. Both the theoretical study of normal families of theoretical significance, but also has important application value.The third phase should go back to Israeli mathematician L. Zalcman in a small paper in 1975. In the article, another way he was, starting from the normal criteria are given a family of meromorphic functions necessary and sufficient conditions are not formal. This approach allows the theoretical study of normal family has entered a new world, it is called Zalcman-Pang method. This approach not only eliminated the original value of many previous methods used by the normal criteria of the study become very simple, and established a series of new normal criteria.The normal family of meromorphic functions with shared values or shared functions together is considered normal families of meromorphic functions is an important topic of theoretical research, this work first began to study the Schwick, many scholars at home and abroad after the issue in depth in this area Study.This article describes the issues this year related to this research, divided into three parts:The first chapter is mainly based on knowledge of the value distribution.The second chapter describes the basics of the theory of normal families.The third chapter is the main result, continue to discuss the shared values, shared set of normal family relationships.