整函数差分唯一性
Uniqueness of Difference about Entire Functions
DOI: 10.12677/PM.2019.93049, PDF,    国家自然科学基金支持
作者: 黄小皇, 刘 丹：华南农业大学应用数学研究所，广东 广州
关键词: 整函数；分担小函数；差分多项式；Entire Function； Shared Small Function； Difference Polynomials
摘要: 本文探讨整函数的差分唯一性问题，证明了：设f(z)为开平面有穷级整函数，g（z）=mi（z）f（z+ci）+…+mk（z）f（z+c）为f(z)的差分多项式，其中mi（z）（i=1，2，…，k）为f的整小函数， ci（i=1，2，…，k）k个判别的有穷复数。又设a(z)≢0为f(z)的一个小函数，若f(z)与g(z)分担0，IM分担a(z) ，则f(z)=g(z) 。
Abstract: In this paper, we investigate the uniqueness of difference operators about entire function, and prove: let f(z) be an entire function of finite order, k be some positive integers, let a(z) be a small function of f(z) , and let g（z）=mi（z）f（z+ci）+…+mk（z）f（z+c） be the difference poly-nomial of f(z) , where mi（z）（i=1，2，…，k）  are the small functions of f(z) , and ci（i=1，2，…，k）  are some finite distinct values. If f(z) and g(z) share 0 CM, and share a(z)IM, then f(z)=g(z) .
文章引用：黄小皇, 刘丹. 整函数差分唯一性[J]. 理论数学, 2019, 9(3): 370-376. https://doi.org/10.12677/PM.2019.93049

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