Geodesic
On unicity of meromorphic functions due to a result of Yang - Hua
Archivum mathematicum, Tome 43 (2007) no. 2, pp. 93-103 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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This paper studies the unicity of meromorphic(resp. entire) functions of the form $f^nf^{\prime }$ and obtains the following main result: Let $f$ and $g$ be two non-constant meromorphic (resp. entire) functions, and let $a\in \mathbb {C}\backslash \lbrace 0\rbrace $ be a non-zero finite value. Then, the condition that $E_{3)}(a,f^nf^{\prime })=E_{3)}(a,g^ng^{\prime })$ implies that either $f=dg$ for some $(n+1)$-th root of unity $d$, or $f=c_1e^{cz}$ and $g=c_2e^{-cz}$ for three non-zero constants $c$, $c_1$ and $c_2$ with $(c_1c_2)^{n+1}c^2=-a^2$ provided that $n\ge 11$ (resp. $n\ge 6$). It improves a result of C. C. Yang and X. H. Hua. Also, some other related problems are discussed.
This paper studies the unicity of meromorphic(resp. entire) functions of the form $f^nf^{\prime }$ and obtains the following main result: Let $f$ and $g$ be two non-constant meromorphic (resp. entire) functions, and let $a\in \mathbb {C}\backslash \lbrace 0\rbrace $ be a non-zero finite value. Then, the condition that $E_{3)}(a,f^nf^{\prime })=E_{3)}(a,g^ng^{\prime })$ implies that either $f=dg$ for some $(n+1)$-th root of unity $d$, or $f=c_1e^{cz}$ and $g=c_2e^{-cz}$ for three non-zero constants $c$, $c_1$ and $c_2$ with $(c_1c_2)^{n+1}c^2=-a^2$ provided that $n\ge 11$ (resp. $n\ge 6$). It improves a result of C. C. Yang and X. H. Hua. Also, some other related problems are discussed.
Classification : 30D35
Keywords: entire functions; meromorphic functions; value sharing; unicity 
@article{ARM_2007_43_2_a1,
     author = {Bai, Xiao-Tian and Han, Qi},
     title = {On unicity of meromorphic functions due to a result of {Yang} - {Hua}},
     journal = {Archivum mathematicum},
     pages = {93--103},
     year = {2007},
     volume = {43},
     number = {2},
     mrnumber = {2336962},
     zbl = {1164.30021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2007_43_2_a1/}
}
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Bai, Xiao-Tian; Han, Qi. On unicity of meromorphic functions due to a result of Yang - Hua. Archivum mathematicum, Tome 43 (2007) no. 2, pp. 93-103. http://geodesic.mathdoc.fr/item/ARM_2007_43_2_a1/