Uniqueness Problems Of The Total Derivative For The Meromorphic Functions On The Complex Variables

In1925, R.Nevanlinna founded the famous Nevanlinna theory, he sdutied the un-iqueness problems of the meromorphic functions by using the value distribution theo-ry, and proved the famous Nevanlinna five, four and three values theorems. At the be-ginning of the new century, L.Jin and F.Lü introduced the concept of the total deriva-tive for the meromorphic function on the several complex variables, and got some co-nclusins of total derivative for the meromorphic functions.This paper mainly includes the uniqueness problems of the total derivative forthe entire and meromorphic functions on the complex variables which are guided bythe author’s tutor professor T.B.Cao, this paper includes four parts:The first chapter mainly introduces the history of Nevanlinna theory, the basicknowledge of Nevanlinna theory for the meromorphic functions on the one variableand several variables.The second chapter mainly introduces the problem of the uniqueness of merom-orphic functions.The third chapter mainly introduces some lemmas and uniqueness conclusionsof the total derivative for the entire functions, and gives the proof of theorem.The fourth chapter mainly introduces some lemmas and uniqueness conclusionsof the total derivative for the meromorphic functions, and gives the proof of thetheorems.