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The Uniqueness of Meromorphic Functions with Sharing Value and Small Functions

Author: ShiErJing
Tutor: YaoWeiHong
School: Shanghai Jiaotong University
Course: Complex analysis and its applications
Keywords: Sharing Value Small Function Sharing Small Function Meromorphic Function Shared Value Shared Small Function
CLC: O174.52
Type: Master's thesis
Year: 2012
Downloads: 15
Quote: 0
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Abstract


The uniqueness theory of meromorphic function is mainly to study conditions under which there is only one function or we can obtain a group of functions such that satisfying some relationships and also satisfying the given conditions. The research of involving the shared value and shared small functions properties originated in R.Nevanlinna’s some research work. His groundbreaking research work laid a solid foundation for the uniqueness theory of meromorphic functions. Many international famous mathematicians, for example Xiong Qinglai , Yang Le , E.Mues and so on, have obtained a number of important research results in this respect.As we all know, the Mues Lemma plays a very great role in the uniqueness of meromorphic functions, and many results have been obtained based on this lemma. However, without generalizing the Mues Lemma to small functions, it is not impossible to achieve more results on the research of small functions.In this paper, we present a generalization of the Mues Lemma on small functions and give a counterexample to sure that the fourth one of the Mues Lemma cannot be generalized to the case of small functions. We hope that it may help to motivate research in the direction.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Theory of functions > Complex analysis,complex function > Integer function theory of meromorphic functions of (semi- pure function theory )
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