On asymptotic values of entire functions

Abstract

In the theory of functions, an asymptotic spot of a function is defined to be a pair , where and is a continuous curve such that (, ). In this paper we introduce a new notion of a strong asymptotic spot. Using this notion, we extend some results of Ahlfors (concerning asymptotic spots of entire functions of finite order) to functions of infinite order. We obtain exact estimates for the number of different strong asymptotic spots of entire functions of finite or infinite lower order.