The Relationship Between Meromorphic Functions With Sharing Value Set

In this thesis,Nevanlinna theory as the main research tool.The uniqueness of meromorphic functions involving shared value sets is explored,and the results of predecessors are generalized and improved.The main conclusions are as follows:Let f(z)and g(z)are both nonconstant meromorphic functions,Then1)If f(z)and g(z)share the value set with S={z|z5+z4+1=0} as IM,and?(?,f)+?(?,g)>?,?(0,f)+?(0,g)>?,where ?>13/8,then f(z)=g(z).2)If f(z)and g(z)share the value set with S={?|?n+?n-1+1=0} as IM,and?(?,f)+?(?,g)>?,?(0,f)+?(0,g)>?,where ?>13/8,,let be an integer not less than 4,then f(z)=g(z).3)If f(z)and g(z)share the value set with S={?|P(?)=?n-1(?+a)-b=}(4?n?29 n ? N+)as IM,where a,bis the constant such that p(co)only takes simple zero point,?(?,f)+?(?,g)>?,?(0,f)+?(0,g)>?,?>30-n/14,then f(z)=g(z).