涉及实零点的亚纯函数的Picard型定理Ⅱ  

Picard Theorem Ⅱ of Meromorphic Functions with Real Zeros

作　　者：赵海燕 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》2017年第4期307-312,共6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：利用亚纯函数的值分布理论和正规族理论的基本知识、研究方法及研究成果,在徐成雨、刘晓俊的一个定理基础上进一步考虑例外函数是有理函数的情况,得到了如下定理:设f为复平面C上的超越亚纯函数,若存在M≥0,使f满足:f=0=〉|z^2f′|≤M;f的零点均为实数;f的极点重级至少为3,则f′-1/z^2有无穷多个零点.By using some fundamental knowledge, research methods and research results about the theories of value distribution and normal family for meromorphic functions and based on one result of Xu Chengyu, Liu Xiaojun＇ s theorem, and by further considering the condition that the exceptional function is a rational function, the following result was achieved： let f be a transcendental meromorphic function on C,if there exists M≥0 such that for f, f = 0：：〉｜ z2 f＇｜ M,all zeros of f are real zeros and all of whose poles have multiplicity at least 3, then f＇ 1/Z^2-; has infinite number of zeros.

关 键 词：超越亚纯函数 实零点 Picard型定理 正规族 

分 类 号：O174.52[理学—数学]