关于亚纯函数的奇异方向

ON THE SINGULAR DIRECTION OF MEROMORPHIC FUNCTION

对以∞为重值的亚纯函数结合导数涉及重值的研究,顾永兴已获得了正规定则。杨乐预示相应于此定则的亚纯函数的奇异方向是存在的,但至今还没有解决这个问题。本文考虑无穷级情形,证实了奇异方向的存在性,并得到对于无穷级亚纯函数f,f′f^m(m>2)的Bofel方向也是存在的。此外还得到一些其它结果。

Gu Yongxing had obtained the normal rule of meromorphie function combining its derivative and involving multiple values. Later Yang Lo predicted the existence of the singular direction of the meromorphic function corresponding to Gu's normal rule. But it hasn't been solved up to now. The paper taking the singular direction of meromorphic function of infinite order into considretion, proves its existence and that obtains the existence theorem of Borel direction of f'f^m(m>2),if f(z) is a meromorphic function of infinite order, Besides, it contains some other results.