亚纯函数及其k阶导数权分担两个公共值的唯一性

Uniqueness of Meromorphic Function with Its k-th Derivative,Sharing Two Weighted Values

用权分担的思想,并通过限制亚纯函数f的极点重数,考察f及其k阶导数分担两个公共值的唯一性问题,改进了Frank-Weissenborn的结果,证明了若非常数亚纯函数f及其k阶导数分担(a,∞),(b,1)且f的极点重数大于等于2k+4,则f≡f(k).

By using the method of weighted sharing values, the result of Frank Weissenborn was improved. Assuming f as a non-constant meromorphic function,and a and b as two distinct finite non-zero values, if f and f（k） share （ a, ∞） and （ b, 1）,and the multiplicity of poles of f≥2 k ＋ 4, then f（k）.