On The Uniqueness Of Meromorphic Functions Concerning Shared Values And Sets

In this thesis,using Nevanlinna theory as the main research tool,this thesis mainly studies two aspects of the uniqueness of meromorphic functions.On the one hand,we study the uniqueness theorem of meromorphic functions with share on value IM.We get the following conclusions:·If nonconstant entire function f(z)and g(z)share the value 1 IM,and(?).Then f(z)?g(z)or f(z)·g(z)?1.·If nonconstant meromorphic function f(z)and g(z)share the value 1 IM,and?(?,f)+?(?,g)+?(0,f)+?(0,g)>11/3,Then T(r,f)=T(r,g)+O(1),(r(?)E,r??.mesE<+?).On the other hand,the uniqueness of meromorphic functions on complex plans involving shared value sets is investigated.The following conclusiong are obtained:Let S={w|P(w)=wn-1(w+a)-b=0},(n=1,2,…),a,b are constants such that P(w)take only single zeros,f(z)and g(z)are two nonconstant meromorphic functions.·When n?3,if E(S,f)=E(S,g),?(0,f)+?(?,f)>7/4,?(0,g)+?(?,g)>7/4,Then T(r,f)=T(r,g)+O(1),(r(?)E,r??,mesE<+?).