具有四个有穷的IM公共小函数的整函数

Entire Functions that Share Four Finite Slowly Growth Meromorphic Functions IM

本文证明了两个非常数整函数若具有四个有穷的ＩＭ公共小函数，则它们必恒等．从而在整函数的情形下，Ｎｅｖａｎｌｉｎｎａ五值定理中的五个ＩＭ公共值能否更换为五个ＩＭ公共小函数（含∞）的问题的回答是肯定的．

In this paper, we prove the following result: Let f and g be two nonconstant entire functions, while c j(z) (∞)(j=1,2,3,4) be four distinct meromorphic functions which satisfy T(r,c j(z))=S(r,f),T(r,c j(z))=S(r,g)(j=1,2,3,4) . Assume {z:f(z)=c j(z)}={z:g(z)=c j(z)}(j=1,2,3,4) , then f≡g .