Growth regularity for the arguments of meromorphic in $\mathbb C\setminus\{0\}$ functions of completely regular growth

Abstract

We study the asymptotic behaviour for the arguments of meromorphic function in $\mathbb C\setminus\{0\}$ of completely regular growth with respect to a growth function $\lambda$. We find that that the key role in the description of this behaviour is played by the function $\lambda_1(r)=\int_1^r\lambda(t)/t\,dt$.