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) ， a 1(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)+a 1(z)f (z)−a(z)f k(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), a 1(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) + a 1(z)f(z) − a(z)f k(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

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