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.