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Title: 探討半純函數指定兩個值之相關問題
On meromorphic functions with two prescribed values
Authors: 張靜華
Chang, Ching Hua
Contributors: 陳天進
Chen, Ten Ging
Chang, Ching Hua
Keywords: 半純函數
Prescribed Values
Date: 2009
Issue Date: 2016-05-09 15:25:42 (UTC+8)
Abstract: 在這篇論文裡,我們探討半純函數指定兩個值之相關問題。特別地,我們探討純函數指定0-1集,同時,我們論證了有關離散型複數數列之一些有趣的結果,利用它們得到關於指定0-1集純函數存在性的必要條件。
In this thesis, we study meromorphic functions with two prescribed values. Especially, entire functions with prescribed zero-one sets. Also, we develop the growth criterion for discrete complex sequences and obtain some interesting results. Using the order of discrete sequences, we obtain a necessary condition for the existence of entire functions with prescribed zero-one set.
謝辭 i
Abstract ii
中文摘要 iii
Introduction 1
Meromorphic Functions with Prescribed Zero-Pole Sets 2
The Growth of Discrete Sequences 6
Basic Theory of Value Distribution 18
Entire Functions with Prescribed Zero-One Sets 25
References 34
Reference: [1] L. V. Ahlfors, Complex analysis, Third edition,McGraw-Hill, 1979.
[2] J. B. Conway, Functions of one complex variable, Second
edition, Springer-Verlag, 1973.
[3] F. Gross, Factorization of meromorphic functions, U. S.
Government Printing Office, Washington, D. C. , 1972.
[4] W. K. Hayman, Meromorphic functions, Clarendon Press,
Oxford, 1964.
[5] R. Nevanlinna, Le theoreme de Picard-Borel et la theorie des fonctions meromorphes, Gauthiers-Villars,
Paris, 1929.
[6] M. Ozawa, On the zero-one set of an entire function, Kodai Math. J. , 2 (1979), 194--199.
[7] L. A. Rubel and C. C. Yang, Interpolation and unavoidable families of meromorphic functions, Mich. Math. J. , 20 (1973), 289--296.
[8] L. Yang, Value distribution theory, Berlin Heidelberg:
Springer-Verlag, Beijing:Science Press, 1993.
[9] C. C. Yang and C. T. Chuang, Fixed points and factorization theory of meromorphic functions, Peking Univ. Press, 1988.
[10] C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, 2003.
[11] H. X. Yi, Some theorems on systems of meromorphic
functions, J. Shandong Univ. , 32 (1997), No.3, 241--247.
Description: 碩士
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Data Type: thesis
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