Julia directions of entire functions of smooth growth

Abstract

Let f(z) be entire i.e. analytic in the finite whole plane Z. The order of f(z) is defined aswhere A ray χ(θ) = {z = r·eiθ : 0 < r < + ∞} is called a Julia direction of f(z) if, in any open sector containing the ray, f(z) takes all values of Z, with at most one finite exceptional value, infinitely often.