零级亚纯函数与其q-差分的唯一性

Uniqueness of Meromorphic Functions of Zero Order with Its q-Difference

运用值分布理论的相关知识研究亚纯函数f(z)与其q-差分的值分担问题,对陈省江得到的超级小于1的非常数亚纯函数与其差分分担两个或三个值的唯一性定理进行了推广,并得到结论:零级亚纯函数f(z)与f(qz)在部分分担(或单边分担)值及N(r,f)=S1(r,f)的条件下,有f(z)≡f(qz).

In this paper,we mainly discuss the sharing value problem of meromorphic function f(z) with its q-difference by using the knowledge of value distribution theory,and generalize the uniqueness theorem of the non-constant meromorphic function of hyper-order less than 1 with its difference share two or three values which obtained by Chen. And we show that if the zero-order meromorphic function f(z) satisfies the condition of sharing values partially or values unilaterally with f(qz) and N(r,f)=S(r,f),then f(z)≡f(qz).