A Proof On The Existence Of The Nevanlinna Direction

The existence of singular direction of meromorphic functions is a very meaningful research theory of angular distributions.In 1983, China’s famous mathematician Zhang Guanghou, Lv Yinian gave the first definition of the Nevanlinna direction. The function f(z) which on the plane will have at least one Nevanlinna direction of Δ (φ) if satisfied =+∞ andIn 1986, Sun Daochun revised the definition of the direction of the deficit and redefine the Nevanlinna direction on the plane. The f(z) will have at least have one Nevanlinna direction if satisfied the condition:I proof the theorem by using the method of dividing the complex plane into a finite angular domain.The existence of the Nevanlinna direction of the function f(z) is discussed under the definition of the direction by Sun Daochun. Compared with the conclusion of Lv Yinian and Zhang Guanghou, the paper proves the existence condition of the method. Compared with Sun Daochun’s method, the complicated calculation process is simplified. In this paper, I have proof that f(z) at least has a Nevanlinna direction of Δ(φ) on the plane if satisfied...