# On unicity of meromorphic functions due to a result of Yang - Hua

Archivum Mathematicum (2007)

• Volume: 043, Issue: 2, page 93-103
• ISSN: 0044-8753

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## Abstract

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This paper studies the unicity of meromorphic(resp. entire) functions of the form ${f}^{n}{f}^{\text{'}}$ and obtains the following main result: Let $f$ and $g$ be two non-constant meromorphic (resp. entire) functions, and let $a\in ℂ\setminus \left\{0\right\}$ be a non-zero finite value. Then, the condition that ${E}_{3\right)}\left(a,{f}^{n}{f}^{\text{'}}\right)={E}_{3\right)}\left(a,{g}^{n}{g}^{\text{'}}\right)$ implies that either $f=dg$ for some $\left(n+1\right)$-th root of unity $d$, or $f={c}_{1}{e}^{cz}$ and $g={c}_{2}{e}^{-cz}$ for three non-zero constants $c$, ${c}_{1}$ and ${c}_{2}$ with ${\left({c}_{1}{c}_{2}\right)}^{n+1}{c}^{2}=-{a}^{2}$ 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.

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