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| 研究生： |
李懿雲 |
|---|---|
| 論文名稱： |
有限秩之半純函數之唯一性 On the Unicity of Meromorphic Functions of Finite Order |
| 指導教授： | 陳天進 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2007 |
| 畢業學年度： | 96 |
| 語文別： | 英文 |
| 論文頁數： | 29 |
| 中文關鍵詞： | 半存函數 |
| 相關次數： | 點閱：120 下載：64 |
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在這篇論文中，我們利用值分布的理論探討有理函數、純函數與半純函數共值的問題及唯一性。同時，我們詳細證明某些已知的結果，並且得到一些性質。
In this thesis, we study the the unicity of rational, entire and meromorphic functions which share common values. Also, we provide more detail proofs of some known results in the literature and obtain some further properties in these aspects.
謝辭 i
Abstract ii
中文摘要 iii
1 Introduction 1
2 Basic Nevanlinna Theory 3
3 Unicity of rational Functions 9
4 Unicity of Entire Functions 14
5 Unicity of Meromorphic Functions 19
References 22
[1] W. W. Adams and E. G. Straus, Non-Archimedian Analytic Functions taking the same values at the same points, Ill.J. Math. ,15(1971), 418-424.
[2] F. Gross, Factorization of Meromorphic Functions, U.S. Government printing Office, Washington, D. C.(1972).
[3] G. G. Gundersen, Meromorphic Functions that Share Three or Four Values, J. London Math. Soc. 20(1979), 457-466.
[4] G. G. Gundersen, Meromorphic Functions that Share Three or Four Values, Trans. Amer. Math. Soc. 277(1983), 545-567.
[5] W. K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964.
[6] R. Nevanlinna, Le théoréme de Picard-Borel et la théorie deo functions méromorphes, Gauthies-Villar, Paris, 1929.
[7] M.Ozawa, Unicity Theorems for Entire Functions, J. D’Anal. Math., 30(1976), 411-420.
[8] G. Pólya, On an Integral Function of an Integral Function, J. London Math. Soc. 1(1926), 12.
[9] C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Science Press (2003).
[10] H. X. Yi, Unicity Theorems for Meromorphic Functions of finite lower order, J. Shandong Univ., 31(1996), NO.3, 241-247.