涉及零点个数的亚纯函数的正规定则
A Normal Criterion of MeromorphicFunctions Concerning Zero Numbers
DOI: 10.12677/PM.2024.147292, PDF,    国家自然科学基金支持
作者: 张泽平, 杨锦华：新疆师范大学数学科学学院，新疆 乌鲁木齐
关键词: 亚纯函数；正规定则；零点个数；Meromorphic Function； Normal Criterion； Zero Numbers
摘要: 设 F 为区域 D 内的一族亚纯函数, a(z)(≢ 0) ， a1(z) 和 b(z) 为区域 D 内的全纯函数。 当 a(z) = 0 时， f (z) ≠ ∞。对于 F 中的每一个函数 f 和正整数 k (k ≥ 4) ，满足 f′(z)+a1(z)f (z)−a(z)fk(z)− b(z) 在区域 D 内至多有 1 个零点(忽略重级)，则 F 在 D 内正规。
Abstract: Let F be a family of meromorphic functions on a domain D, a(z)(≢ 0), a1(z) and b(z) are holomorphic functions on D. If k is a positive integer and k ≥ 4, ∀f∈F, f (z) ≠ ∞ when a(z) = 0, f′(z) + a1(z)f(z) − a(z)fk(z) − b(z) has at most 1 zeros (ignoring multiplicity), then F is normal on D.
文章引用：张泽平, 杨锦华. 涉及零点个数的亚纯函数的正规定则[J]. 理论数学, 2024, 14(7): 266-274. https://doi.org/10.12677/PM.2024.147292

参考文献

[1] Hayman, W.K. (1967) Research Problems of Function Theory. Athlone Press of University of London.
[2] Yang, J.H., Yang, Q. and Pang, X.C. (2019) A Normal Criterion Concerning Omitted Holo- morphic Function. Acta Mathematica Sinica, English Series, 35, 1972-1978.[CrossRef] 
[3] 杨锦华, 庞学诚. 涉及微分多项式的正规定则献给杨乐教授80华诞[J]. 中国科学: 数学, 2019, 49(10): 1439-1444.
[4] Sun, C. (2021) A Normal Criterion Concerning Zero Numbers. Rendiconti del Circolo Matem- atico di Palermo Series 2, 72, 515-523. [Google Scholar] [CrossRef] 
[5] Pang, X. and Zalcman, L. (2000) Normal Families and Shared Values. Bulletin of the London Mathematical Society, 32, 325-331. [Google Scholar] [CrossRef] 
[6] Long, H. (1990) On Normal Criterion of Meromorphic Functions. Science in China Series A| Mathematics, Physics, Astronomy & Technological Science, 33, 521-527. [Google Scholar] [CrossRef] 
[7] Zhang, G., Pang, X. and Zalcman, L. (2009) Normal Families and Omitted Functions II. Bulletin of the London Mathematical Society, 41, 63-71. [Google Scholar] [CrossRef] 
[8] Fang, M.-L. (2001) Picard Values and Normality Criterion. Bulletin of the Korean Mathemat- ical Society, 38, 379-387.
[9] Wang, Y. and Fang, M. (1998) Picard Values and Normal Families of Meromorphic Functions with Multiple Zeros. Acta Mathematica Sinica, 14, 17-26.[CrossRef] 
[10] Chang, J. (2010) Normality of Meromorphic Functions Whose Derivatives Have 1-Points. Archiv der Mathematik, 94, 555-564. [Google Scholar] [CrossRef] 
[11] Deng, B., Qiu, H., Liu, D. and Fang, M. (2013) Hayman's Question on Normal Families Concerning Zero Numbers. Complex Variables and Elliptic Equations, 59, 616-630.[CrossRef] 
[12] Pang, X., Yang, D. and Zalcman, L. (2003) Normal Families of Meromorphic Functions Whose Derivatives Omit a Function. Computational Methods and Function Theory, 2, 257-265.[CrossRef] 
[13] Chang, J. (2013) Normality of Meromorphic Functions and Uniformly Discrete Exceptional Sets. Computational Methods and Function Theory, 13, 47-63.[CrossRef] 

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