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Zbl 1186.30037
Xu, Junfeng; Han, Qi; Zhang, Jilong
Uniqueness theorems of meromorphic functions of a certain form.
(English)
[J] Bull. Korean Math. Soc. 46, No. 6, 1079-1089 (2009). ISSN 1015-8634

Author's abstract: We show that, for any entire function $f$ and all positive integers $m, n\in \Bbb{N}$, possibly except for the special case $m=n=1$, the function $f^m(f^n-1)f^{\prime}$ has no non-zero finite Picard value. Furthermore, we show that, for any two non-constant meromorphic functions $f$ and $g$, if $f^m(f^n-1)f^{\prime}$ and $g^m(g^n-1)g^{\prime}$ share the value 1 weakly, then $f\equiv g$ provided that $m$ and $n$ satisfy some conditions. In particular, if $f$ and $g$ are entire, then the restrictions on $m$ and $n$ can be greatly reduced.
[Kazuya Tohge (Kanazawa)]
MSC 2000:
*30D35 Distribution of values (one complex variable)
30D20 General theory of entire functions
30D30 General theory of meromorphic functions

Keywords: entire function; meromorphic function; Picard value

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