Uniqueness of meromorphic functions on ℂ

  • Pei-Chu Hu
  • Ping Li
  • Chung-Chun Yang
Part of the Advances in Complex Analysis and its Applications book series (ACAA, volume 1)

Abstract

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 [1], [200], [196], [281] and [280]). For instances, M. Ozawa [198] studied the properties of entire functions that share two values, while L. A. Rubel and C. C. Yang [210] studied the problems on entire functions which share two values with its derivative. G. G. Gundersen [85] and E. Mues [179] 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 [297] 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.

Keywords

Entire Function Nonzero Constant Uniqueness Relate Small Function Differential Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Pei-Chu Hu
    • 1
  • Ping Li
    • 2
  • Chung-Chun Yang
    • 3
  1. 1.Department of MathematicsShandong UniversityJinan, ShandongChina
  2. 2.Department of MathematicsUniversity of Science and Technology of ChinaHefei, AnhuiChina
  3. 3.Department of MathematicsThe Hong Kong University of Science and TechnologyHong KongChina

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