| 杨刘.多复变整函数与其关于全导数的微分多项式*[J].数学年刊A辑,2021,42(4):349~358 |
| 多复变整函数与其关于全导数的微分多项式* |
| Entire Function of Several Complex Variables and Its Differential Polynomial on Total Derivatives |
| Received:April 25, 2020 Revised:August 22, 2021 |
| DOI：10.16205/j.cnki.cama.2021.0027 |
| 中文关键词: 整函数, 全导数, 分担值, 唯一性 |
| 英文关键词:Entire function, Total derivative, Sharing value, Uniqueness theorem |
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| 中文摘要: |
| 本文证明如下定理: 设f为Cn上的一个非常数整函数,LD(f) = akDkf +ak?1Dk?1f +· · · + a1Df + a0f,其中aj ∈ C, ak ≠ 0, Dj f是f的j阶全导数(j=1,2, · · ·,k).若f与LD(f)两个有穷的CM分担值, 则f=LD(f). |
| 英文摘要: |
| In this paper, the author proves the following theorem: If a nonconstant entire function f and its differential polynomial LD(f) share two distinct CM values, then f ≡ LD(f), where LD(f)=akDkf +ak?1Dk?1f +· · · + a1Df + a0f,with aj ∈ C, ak ≠ 0, and Dj f is the j-th order total derivative of f, j = 1, 2, · · · , k. |
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