The Growth Of Meromorphic Functions And The Existence Of T Direction For Algebroidal Functions

The aim of this thesis is to consider some problems related to the growth of meromorphic functions and the existence of a new singular direction( T direction) for algebroidal functions. Our main works are as follows:In chapter 1, we introduced some common signs, basic knowledge and fundamental theorems concerning the problems that we discussed in the thesis.In chapter 2, we investigated the argument distribution and growth of meromorphic functions under the restriction of some cohditions for zeros of the meromorphic fuction and 1-points of its derivative, and obtained a more precise estimation toward growth of meromorphic functions.In the other chapters, we proved the existence of a new singular direction (T direction) for algebroidal functions under different conditions. As concerning the T direction, the characteristic function T(r,w) is used as a comparison function. In chapter 3, we studied the existence of T direction for zero order algebroidal function w(z) with v value. In addition, the relation between maximum Borel direction and T direction was given. In chapter 4, we argued the existence of T direction for infinite order algebroidal function w(z) with v value. Synchronously,the relation between maximality Borel direction and T direction was given. In chapter 5, we testified the existence of T direction for the zero order algebroidal function w(z) in the unit circle.