# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
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 $\lambda$, $\arg z = \theta\sb j$ $(0 \le \theta\sb 1 < \theta\sb 2 < \cdots < \theta\sb q < 2 \pi$, $\theta\sb{q + 1} = \theta\sb 1 + 2 \pi)$ be a finite number of rays, $n$ be the counting function of zeros of the function $ff'-1$. If $f$ satisfies $$\varlimsup\sb{r \to \infty} {\log \sum\sp q\sb{j = 1} n(r, \theta\sb j + \varepsilon, \theta\sb{j + 1} - \varepsilon) \over \log r} \le \rho$$ for any small positive number $\varepsilon$, then $$\lambda \le \max \left( {\pi \over \theta\sb 2 - \theta\sb 1}, \dots, {\pi \over \theta\sb{q + 1} - \theta\sb q}, \rho \right).$$ 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 [{\it A. A. Gol’dberg}, {\it J. V. Ostrovskii}, The distribution of values of meromorphic functions. Moskva: Nauka (1970; Zbl 0217.10002) (Russian), chapter III, § 3] is used.

##### MSC:
 30D15 Special classes of entire functions; growth estimates 30D35 Distribution of values (one complex variable); Nevanlinna theory