亚纯函数位移多项式的值分布
On Value Distribution of Shift Polynomials of Meromorphic Functions
DOI: 10.12677/PM.2022.127126, PDF,    国家自然科学基金支持
作者: 成奇斌, 李叶舟：北京邮电大学，理学院，北京
关键词: 亚纯函数；位移多项式；值分布；特征函数；亏量；Meromorphic Function； Shift Polynomial； Value Distribution； The Characteristic Function； Deficiency
摘要: 设f是非常数亚纯函数，Pn(z,f)是关于f的一类线性位移多项式，β是f的小函数。本文借助差分形式Nevanlinna值分布理论，研究了f与Pn(z,f)-β(z)的特征函数之间的关系、Pn(z,f)与Pn(z,f)-β(z)的亏量等值分布性质，部分地推广了现有的一些结果。
Abstract: Let f be a nonconstant meromorphic function, Pn(z,f) be a shift polynomial of f, β be a small function with respect to f. With the help of difference version of Nevanlinna theory, some existing results could be partially generalized through studying the value distribution properties of Pn(z,f), such as the relationship between the characteristic functions of f and Pn(z,f)-β(z), the deficiencies of Pn(z,f) and Pn(z,f)-β(z).
文章引用：成奇斌, 李叶舟. 亚纯函数位移多项式的值分布[J]. 理论数学, 2022, 12(7): 1146-1159. https://doi.org/10.12677/PM.2022.127126

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