与差分相关的整函数周期性问题
Periodicity of Entire Functions Concerning Difference
DOI: 10.12677/PM.2020.102015, PDF,  被引量    国家自然科学基金支持
作者: 邓炳茂：广东金融学院，金融数学与统计学院，广东 广州；杨世伟：华南农业大学，应用数学研究所，广东 广州
关键词: 整函数；Picard例外值；周期函数；Entire Function； Picard Exceptional Value； Periodic Function
摘要: 本文主要研究了有穷级整函数与差分相关的周期性问题，主要证明了：如果f(z)是有穷级超越整函数，d是f(z)的一个Picard例外值，如果f(z)Δcf(z)是周期函数，则f(z)也是周期函数。
Abstract: This paper studied the periodicity of entire functions with its difference, and proved: Let f(z) be a transcendental entire function of finite order, and d be a Picard exceptional value of f(z). If f(z)Δcf(z) is a periodic function, then f(z) is also a periodic function.
文章引用：邓炳茂, 杨世伟. 与差分相关的整函数周期性问题[J]. 理论数学, 2020, 10(2): 96-99. https://doi.org/10.12677/PM.2020.102015

参考文献

[1] 杨乐. 值分布及其新研究[M]. 北京: 科学出版社, 1982: 5-13.
[2] Yang, C.C. and Yi, H.X. (2003) Uniqueness Theory of Meromorphic Functions. Science Press, Beijing, 1-13. [Google Scholar] [CrossRef] 
[3] Hayman, W.K. (1964) Mermorphic Functions. Clarendon Press, Oxford, 4-10.
[4] 王琼, 扈培础. 关于整函数零点和周期性的研究[J]. 数学物理学报, 2018, 38(2): 209-204.
[5] Liu, K. and Yu, P.Y. (2019) A Note on the Periodicity of Entire Functions. Bulletin of the Australian Mathematical Society, 100, 290-296. [Google Scholar] [CrossRef] 
[6] Chiang, Y.M. and Feng, S.J. (2008) On the Nevanlinna Characteristic of f(z+η) and Difference Equations in the Complex Plane. The Ramanujan Journal, 16, 105-129. [Google Scholar] [CrossRef] 

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