| 陈创鑫,张然然.涉及整函数差分算子的唯一性定理[J].数学年刊A辑,2021,42(1):11~22 |
| 涉及整函数差分算子的唯一性定理 |
| Uniqueness Theorems Related to Difference Operators of Entire Functions |
| Received:March 19, 2020 Revised:September 24, 2020 |
| DOI：10.16205/j.cnki.cama.2021.0002 |
| 中文关键词: 差分算子, 整函数, Borel 例外值, 分担值 |
| 英文关键词:Difference operator, Entire function, Borel exceptional value, Sharing value |
| 基金项目:国家自然科学基金(No.,11801093), 广东省青年创新人才项目(No.,2018KQNCX117),广东省特色创新项目(No.,2019KTSCX119)和广东省自然科学基金(No.,2018A030313508, No.,2020A1515010459) |
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| 中文摘要: |
| 作者研究了关于有穷级整函数两个差分算子的分担值问题, 证明了: 令f(z) 是满足 lambda(f-a(z)) |
| 英文摘要: |
| In this paper, the authors study the shared-value problem concerning two difference operators of an entire function with finite order. They prove that: Let f(z) be a finite order transcendental entire function such that λ(f ?a(z)) < ρ(f), where a(z) (∈ S(f)) is an entire function and satisfies ρ(a(z)) < 1, and let η (∈ C) be a constant such that ?2ηf(z) 6≡ 0.If ?2ηf(z) and ?ηf(z) share ?ηa(z) CM, where ?ηa(z) ∈ S(?2ηf(z)), thenf(z) = a(z) + BeAz,where A, B are two nonzero constants and a(z) reduces to a constant. |
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