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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