涉及重级的亚纯函数族的正规定则

Normality criterion of families of meromorphic functions with multiple zeros and poles

针对徐焱的定理给出了其逆命题成立的条件,进一步改进了Hayman猜想.并得到了新的正规定则:k∈N,设F是D内亚纯函数族,f∈F在D内的零点之级≥k+2,极点之级≥2,h(z)■0是D上的亚纯函数,若f(k)(z)≠h(z),z∈D,则F在D内正规.

The requirement of conversepro position on the basis of theorm given by Xu Yan was found,and the Hayman conjecture was further improved,then a new normal criterion was obtained：Let F be a family of meromorphic function in a complex domain D.Let k∈N,for f∈F,with multiple of zeros at least k＋2 and poles at least 2,h（z）（ 0） a meromorphic function in D,for z∈D,if f（k）（z）≠h（z）,then F is a normal family in D.