Uniqueness of meromorphic functions on ℂ
Combining value distribution theory and the classical function theory to study uniqueness theorems of meromorphic functions has become an interesting and active field in recent years. Nevanlinna himself proved his famous five-value theorem and four-value theorem right after his establishment of the value distribution theory around 1924. Since then, there appeared no significant studies on sharing values of meromorphic functions or entire functions till 1970s, several mathematician started the research in this topic (see , , ,  and ). For instances, M. Ozawa  studied the properties of entire functions that share two values, while L. A. Rubel and C. C. Yang  studied the problems on entire functions which share two values with its derivative. G. G. Gundersen  and E. Mues  weakened the conditions of R. Nevanlinna’s four-value theorem. Since 1980s, there have many papers been published on uniqueness theory and sharing values, and a comprehensive Chinese monograph  was appeared in 1995. In the present chapter, we introduce and summarize some of the more recent and relatively new results on value sharing and uniqueness theory on ℂ.
KeywordsEntire Function Nonzero Constant Uniqueness Relate Small Function Differential Polynomial
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