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Unicity theorems for two meromorphic functions with their first derivatives having the same 1-points. (Chinese) Zbl 0736.30021
If \(f-a\) and \(g-a\) have the same zeros with the same multiplicities, we write \(f=a\rightleftarrows g=a\). The authors correct K. Shibazaki’s result [Mem. Natl. Def. Acad. 21, 67-71 (1981; Zbl 0507.30022)]. Then they prove the following theorem: Suppose that \(f\), \(g\) are two non- constant meromorphic functions. If their deficiencies \(\delta(0,f)+\delta(0,g)>1, \delta(\infty,f)=\delta(\infty,g)=1\), and \(f'=1\rightleftarrows g'=1\), then \(f\equiv g\) or \(f'g'\equiv 1\). This theorem answers C. C. Yang’s question [M. Ozawa, J. Analyse Math. 30, 411-420 (1976; Zbl 0337.30020)].

MSC:
30D30 Meromorphic functions of one complex variable, general theory
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