涉及实零点的亚纯函数Picard型定理  

Picard Theorem of Meromorphic Functions with Real Zeros

作　　者：徐成雨 刘晓俊[1] 

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《上海理工大学学报》2016年第5期414-418,共5页Journal of University of Shanghai For Science and Technology

基　　金：国家自然科学基金青年基金资助项目(11401381)

摘　　要：利用亚纯函数的正规理论和值分布理论的基本概念、研究方法以及研究成果,并以Marty正规定则为基础,对零点均是实数的亚纯函数的Picard型定理进行了研究,得到:设d∈N^+,f是复平面瓘上的超越亚纯函数,若存在M≥0,使得f满足f的零点均为实数;f的极点重级至少为3;当f(z)=0时,必有|f′(z)|≤M|z^d|,则f′-z^d有无穷多个零点.By virtue of some fundamental concepts,analysis methods and research results about the theories of value distribution and normal family for meromorphic functions and based on Marty＇s criterion for normality,the Picad theorem of meromorphic functions with real zeros was discussed and it is proved：let d∈N＋,f be a transcendental meromorphic function on the complex plane C,if there exists M ≥0,so that for f,all zeros of f are real number,all of whose poles have multiplicity at least 3 and f（z）=0■｜f′（z）｜ ≤M｜zd｜,then f′-z^d has infinite zeros.

关 键 词：亚纯函数 正规族 实零点 Picard型定理 

分 类 号：O174.52[理学—数学]