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Angular distribution of values of ff ' . (English) Zbl 0804.30024

The main result of the authors is the following: Theorem 1. Let f(z) be an entire function of finite order λ, argz=θ j (0θ 1 <θ 2 <<θ q <2π, θ q+1 =θ 1 +2π) be a finite number of rays, n be the counting function of zeros of the function ff ' -1. If f satisfies

lim ¯ r log j=1 q n(r,θ j +ε,θ j+1 -ε) logrρ

for any small positive number ε, then

λmaxπ θ 2 -θ 1 ,,π θ q+1 -θ q ,ρ·

Lemma 1 (there must be changed O(1) to O(logr) in the text of the lemma), which is cited by the authors as the result of Nevanlinna, is the hypothesis of Nevanlinna has yet to be demonstrated. I think that in place of the Lemma 1, the theorem 3.1 [A. A. Gol’dberg, J. V. Ostrovskii, The distribution of values of meromorphic functions. Moskva: Nauka (1970; Zbl 0217.10002) (Russian), chapter III, §3] is used.

MSC:
30D15Special classes of entire functions; growth estimates
30D35Distribution of values (one complex variable); Nevanlinna theory