Angular distribution of values of \(ff'\)
The main result of the authors is the following: Theorem 1. Let \(f(z)\) be an entire function of finite order \(\lambda\), \(\arg z = \theta_ j\) \((0 \leq \theta_ 1 < \theta_ 2 < \cdots < \theta_ q < 2 \pi\), \(\theta_{q + 1} = \theta_ 1 + 2 \pi)\) be a finite number of rays, \(n\) be the counting function of zeros of the function \(ff'-1\). If \(f\) satisfies \[ \varlimsup_{r \to \infty} {\log \sum^ q_{j = 1} n(r, \theta_ j + \varepsilon, \theta_{j + 1} - \varepsilon) \over \log r} \leq \rho \] for any small positive number \(\varepsilon\), then \[ \lambda \leq \max \left( {\pi \over \theta_ 2 - \theta_ 1}, \dots, {\pi \over \theta_{q + 1} - \theta_ q}, \rho \right). \] Lemma 1 (there must be changed \(O(1)\) to \(O (\log r)\) 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 [\textit{A. A. Gol'dberg}, \textit{J. V. Ostrovskii}, The distribution of values of meromorphic functions. Moskva: Nauka (1970; Zbl 0217.10002) (Russian), chapter III, \S 3] is used.
scientific article; zbMATH DE number 589844