整函数与其差分算子分担集合的唯一性问题

考虑整函数与其差分算子分担集合的唯一性问题.假设S={ω:ω~n+aw~(n-1)+b=0},m,n为两个正整数满足n2且n和n一m互素,a和b为两个非零复数使得方程ω~n+aw~n+b=0无重根.设f为满足λ(f)ρ(f)∞的非常数整函数,若f(z)和△_cf(z)CM分担集合S,则f(z+c)≡2f(z).这个结果改进了李效敏的定理.

The Uniqueness Problem on Entire Functions Sharing Set with Their Difference Operators

In this paper,we investigate the uniqueness theorem of entire functions sharing sets with its difference operators.Supposed that S:= {w~n +aω~(n-m)+ b = 0},m,n be nonzero district integers such that n > 2 and n,n — m are relatively prime,a,b be two non-zero complex numbers such that equation w~n + aw~(n~m) + b = 0 has no multiple roots.Let f(z) be a nonconstant entire function satisfying λ(f) < p(f) < ∞,if f(z) and △cf(z)share S CM,then f(z+c) =2f(z),which improved Xiao-Min Li's results.