Entire functions with preassigned zero proximate order
  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. 
A. F. Grishin, Nguyen Van Quynh
math.CV