The T-Direction Of Meromorphic Function And Algebroids Function

Singular direction is one of the important parts of the value-distributed theory.Based on the prevenient research of the singular direction for the meromorphic function, in this paper we make use of Ahlfors- Shimizu characteristic function of the meromorphic function to investigate a new sigular direction for the meromorphic function namely T-direction. And expand this unique direction to the algebroids function.In the first chapter we introduce the development process of the singular direction for the meromorphic function briefly and the relevant knowledge. In the second chapter we discuss the existence of the T-direction of the meromorphic function, especially discuss the existence of the corresponding T-direction when the meromorphic function takes the value of its small functions. Here the Ahlfors-Shimizu characteristic function in an angle domain and the geometric meaning of Ahlfors- Shimizu characteristic function play the important role. In the third chapter we discuss the T-direction of a meromorphic function in an unit circle. In the fourth chapter,we discuss the common T-direction of meromorphic function. In the fifth chapter we discuss that as the extension of the meromorphic function the algebroids function also should exist the similar T- direction. And we prove the related result.