涉及零点和微分多项式的全纯函数族的正规定则
Normality Criterion Concerning Zeros and Differential Polynomials for Families of Holomorphic Functions
DOI: 10.12677/pm.2025.158214, PDF,    国家自然科学基金支持
作者: 谭代明, 杨锦华*：新疆师范大学数学科学学院，新疆 乌鲁木齐
关键词: 全纯函数；微分多项式；正规定则；零点个数；Holomorphic Function； Differential Polynomial； Normality Criterion； Zero Numbers
摘要: 本文结合值分布和正规族理论研究了与零点个数和微分多项式有关的一类全纯函数族的正规定则。文章利用经典引理，使用反证法和分类讨论，将涉及零点个数有关的全纯函数正规定则推广到一般的微分多项式，得到一个新的结果，丰富了全纯函数正规族理论。
Abstract: In this paper, the normality criterion of a class of families of meromorphic functions related to the number of zeros and differential polynomials is studied by combining the theories of value distribution and normal families. The article makes use of classical lemmas, and combines the method of proof by contradiction with classification discussion, the normal criteria of meromorphic functions involving the number of zeros is extended to general differential polynomials, and a new result is obtained, which enriches the theory of normal families of meromorphic functions.
文章引用：谭代明, 杨锦华. 涉及零点和微分多项式的全纯函数族的正规定则[J]. 理论数学, 2025, 15(8): 1-7. https://doi.org/10.12677/pm.2025.158214

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