涉及分担集的整函数的唯一性

Uniqueness of Entire Function Related to Shared Set

中文关键词:  ?整函数  正规性  唯一性  分担集  导数.

英文关键词:entire function  normality  uniqueness  shared set  derivative.

中文摘要:

      本文研究了涉及分担集的整函数的唯一性. 设$f$是非常数整函数．若存在具有3个元素集合$S$, $d$为任一有穷复数，$k$为一正整数，$f-d$的零点重数$\geq k 1$, 使得$E(S,f)=E(S,f^(k))$, 则$f=f^(k)$.

英文摘要:

      In this paper, uniqueness of entire function related to shared set is studied. Let $f$ be a non-constant entire function and $k$ be a positive integer, $d$ be a finite complex number. There exists a set $S$ with 3 elements such that if $f$ and its derivative $f^{(k)}$ satisfy $E(S,f)=E(S,f^{(k)})$, and the zeros of $f(z)-d$ are of multiplicity $\geq k 1$, then $f=f^{(k)}$.