涉及亏值的亚纯函数唯一性

On the Uniqueness of the Meromorphic Functions Concerning Deficient Values

结合亚纯函数的亏值，讨论了当高阶导数具有一个分担值或分担函数时两个亚统函数的等价性，得出两点结论：（１）设ｆ与ｇ是两个亚约函数，满足δ（∞，ｆ）＝δ（∞，ｇ）＝１．若对某个ｎ≥１有ｆ（ｎ）与ｇ（ｎ）分担值１，且，则ｆ（ｎ）·ｇ（ｎ）≡１或ｆ－ｇ≡ｋ。（２）设ｆ与ｇ为整函数，满足，若对某个ｎ≥１，ｆ（ｎ）与ｇ（ｎ）分担值１，δ（０，ｆ）＞０且０为ｇ的Ｐｉｃａｒｄ例外值，则ｆ≡ｇ或。

The purpose of this paper is to study from deficient values the identity of two meromorphic functions, the higher derivatives of which share one value or one small function. The following results are obtained which improve some conclusions of Yi Hongxun's. (1) Let f and g be two meromorphic functions satisfying δ(∞,f) =δ(∞,g) =1. If f(n) and g(n) share one value 1 for any n≥1, and , then f(n)·g(n) 1 or f-g≡k, where k is the difference between some deficient values of f and g. (2) let log log log M(r,g)<1. If f(n) and g(n) f and g be two entire functions satisfying limsup share one value 1 for any n≥1, δ(0,f)>0 and g has a Picard's exceptional value 0, then f≡g or g≡beax, , where a and b are two constants.