权分担三个集合的亚纯函数的唯一性

Uniqueness of Meromorphic Functions Weighed Sharing Three Sets

利用权分担集合的思想讨论了关于分担三个集合的亚纯函数的唯一性问题.证明了:设f与g是开平面上两个非常数亚纯函数,ki(i=1,2,3)为非负整数,n为不小于2的整数.若Ek1({1,ω,ω2,…,ωn},f)=Ek1({1,ω,ω2,…,ωn},g)Ek2({0},f)=Ek2({0},g)Ek3({∞},f)=Ek3({∞},g)且a,b,c,n满足(an-a-2)(bcn-b-c)>2bcn,其中k1+1=a,k2+1=b,k3+1=c,则f≡tg(tn=1);或fg≡s(sn=1),且0和∞为f与g的缺省值.

Using the idea of weighted sharing, deal with the uniqueness problems on meromorphic functions that sharing three sets. Mainly the authors proved the following results： Let f and g be two meromorphic functions, ki（i=1,2,3） be non-negative integers, n be an integer not less than 2, and （an-a-2） （bcn-b-c）〉2bcn where k1＋1=a, k2＋1=b, k3＋1=c, then f≡tg where t^n=1 or fg≡s where 0 and ∞ are lacunary values of f and g, and s^n=1.