涉及导数与差分的亚纯函数的小函数的收敛指数与级

王品玲, 杨世伟, 方明亮

数学学报 ›› 2021, Vol. 64 ›› Issue (1) : 77-86.

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PDF(371 KB)
数学学报 ›› 2021, Vol. 64 ›› Issue (1) : 77-86. DOI: 10.12386/A2021sxxb0006
论文

涉及导数与差分的亚纯函数的小函数的收敛指数与级

    王品玲1, 杨世伟2, 方明亮2
作者信息 +

The Exponents and Order of Convergence of Small Functions of Meromorphic Functions Concerning Derivatives and Differences

    Pin Ling WANG1, Shi Wei YANG2, Ming Liang FANG2
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摘要

fz)是一个复平面上的亚纯函数,c是一个非零有穷复数,az)是fz)的一个小函数,本文研究fz)- az),fz+c)- az)及Δcn fz)- az)(n ∈ N+)的零点收敛指数与fz)的级之间的关系.由此改进了涉及导数与差分的亚纯函数值分布的一些相关结果.

Abstract

Let f(z) be a meromorphic function in the complex plane, let c be a nonzero finite complex number, and let a(z) be a small function with respect to f(z). It is studied that the relationship between the exponent of convergence of zeros of f(z)-a(z), f(z + c)-a(z), and Δcn f(z)-a(z) (n ∈ N+) and the order of f(z). This improves some results in value distribution of meromorphic functions concerning derivatives and differences.

关键词

亚纯函数 / 导数 / 差分 / 值分布

Key words

meromorphic functions / derivatives / differences / value distribution

引用本文

导出引用
王品玲, 杨世伟, 方明亮. 涉及导数与差分的亚纯函数的小函数的收敛指数与级. 数学学报, 2021, 64(1): 77-86 https://doi.org/10.12386/A2021sxxb0006
Pin Ling WANG, Shi Wei YANG, Ming Liang FANG. The Exponents and Order of Convergence of Small Functions of Meromorphic Functions Concerning Derivatives and Differences. Acta Mathematica Sinica, Chinese Series, 2021, 64(1): 77-86 https://doi.org/10.12386/A2021sxxb0006

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基金

国家自然科学基金资助项目(11701188,11901119)

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