关于f^nf'-c的值分布

The Value Distribution of f nf-c

设ｆ为超越亚纯函数，ｃ为不恒等于零的ｆ的小函数，本文证得：当ｎ≥３时，ｆｎｆ－ｃ有无穷多个零点；若附加条件ｆ只有有限多个级≤２的零点，则对一切正整数ｎ，ｆｎｆ－ｃ都有无穷多个零点．因而对ＣｈｉａｎｇＹ．Ｍ．的问题作出了部分回答．

Let f be a transcendental meromorphic function and c (0) be a small function of f . It is shown that if n ≥3,then f nf-c has infinitely many zeros and if f has finitely many zeros of order≤2, thcn f nf-c has infinitely many zeros for every positive integers.