华东师范大学学报(自然科学版) ›› 2014, Vol. 2014 ›› Issue (4): 8-17.

• 应用数学与基础数学 • 上一篇    下一篇

关于亚纯函数的k阶导函数和有理函数

杨 拍1, 刘晓俊2   

  1. 1. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China;
    2. Department of Mathematics, University of Shanghai for Science and Technology, Shanghai 200093, China
  • 收稿日期:2013-07-01 修回日期:2013-10-01 出版日期:2014-07-25 发布日期:2014-07-25

On the kth derivatives of meromorphic functions and rational functions

YANG Pai1, LIU Xiao-jun2   

  1. 1. 成都信息工程学院~应用数学学院, 成都 610225;
    2. 上海理工大学~数学系, 上海 200093
  • Received:2013-07-01 Revised:2013-10-01 Online:2014-07-25 Published:2014-07-25

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摘要： 设\,$f$\,是复平面\,$\mathbb C$\,内的超越亚纯函数,
$R$\,是一个有理函数且\,$R \not\equiv0$, $k$\,是一个正整数.
并假设\,$f$\,的零点重级至少为\,$k+1$, 至多有限个零点例外.
则\,$f^{(k)}-R$\,有无限多个零点.

关键词: 亚纯函数, Julia例外函数, 拟正规族

Abstract: Let $f$ be a transcendental meromorphic function in
$\mathbb C$, $R\not\equiv0$
 be a rational function,
 and let $k$ be a positive integer.
 Suppose that all zeros of $f$ have multiplicity at least $k+1$,
 except possibly finite many.
 Then $f^{(k)}-R$ has infinitely many zeros.

Key words: meromorphic function, Julia exceptional function, quasinormal family

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