By using the Nevanlinna's value distribution theory, this dissertation studies the problems of the uniqueness of meromorphic functions in four aspects, and several unicity theorems are obtained. This dissertation studies the uniqueness of entire functions sharing one value with its weight, and the uniqueness of meromorphic functions sharing two values with its weight, and the uniqueness of meromorphic functions sharing one common range sets. The results obtained in this dissertation Improve and generalize the present conclusions.
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