Entire functions with preassigned zero proximate order

Abstract

It is known that if the proximate order $\rho (r)$ such that $\lim \rho (r)=\rho >0(r\to \infty )$, then there exists an entire function $f(z)$ of proximate order $\rho (r)$. In the case where $\rho =0$ the question about the existence of such entire function remained open until now. This question is investigated in the paper.

10 pages, in Russian