With The Family Of Meromorphic Functions Of The Three Shared Value Base

In this paper,we mainly study the uniqueness theory of mero-morphic functions concerning sharing three values.firstly,we study the condition of meromorphic function and entire function with periodicity. A equivalence condition of meromorphic function with periodicity was given.for entire function with periodicity we also gain a sufficient condition.Secondly,a criterion for normality of a family with meromorphic function was obtained.We proved that a family with meromorphic function sharing three values IM is normal. Finally, a problem about the basic number of a family of meromorphic function was solved.We proved that the basic number of a family of rational function sharing three values IM is fmite;the basic number of a family of meromorphic function sharing three values DM is finite.