涉及差分多项式的亚纯函数的唯一性

Uniqueness of meromorphic functions concerning difference polynomials

主要研究了涉及差分多项式的亚纯函数的唯一性问题.假设f(z)为超级小于1的非常数亚纯函数,M(f)=∑pi=0αif(z+iη)是f(z)的一类差分多项式,其中η(≠0),p,α0,α1,…,αp(≠0)均为常数且α0+α1+…+αp=0.若f(z)与M(f)CM分担2个值且IM分担1个值,则f(z)≡M(f).

In this paper,we prove a uniqueness theorem of meromorphic functions concerning difference polynomials.Suppose that f(z)is a non-constant meromorphic function of hyper order less than 1 and M(f)=∑pi=0αif(z+iη) is a difference polynomial of f(z),where η(≠0),p,α0,α1,…,αp(≠0) are constants and α0+α1+…+αp=0.If f(z)and M(f)share two values CM and share one value IM,then f(z)≡M(f).