Deficient Values and Borel Directions of Meromorphic Functions

Abstract

In Chapter 1, we have seen that while Borel direction are basic to angular distribution theory, the concept of a deficient value is important in modular distribution theory, where the definition of a deficient value depends only on the modulii of the points at which the function takes on this value. It would therefore not appear initially to be the case that there is any relationship between Borel directions and deficient values. However, Yang Lo and Zhang Guanghou have shown that if a meromorphic function of finite positive order has a deficient value, then the distribution of its Borel directions has to follow a certain rule. In the general case, the deficient values and Borel directions are closely related to each other in number.