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題名 半純函數共慢成長函數之唯一性
作者 郭玲伶
貢獻者 陳天進
郭玲伶
關鍵詞 半純函數
唯一性
少函數
meromorphic functions
uniqueness
small function
日期 2008
上傳時間 8-十二月-2010 11:46:52 (UTC+8)
摘要 在這篇論文裡，我們利用值分佈理論來探討兩個半純函數何時會相等，進而了解兩個半純函數滿足某一函數方程時，其關係為何。最後，我們探討兩個半純函數共四個少函數且擁有少量的極點之相關性質。
In this thesis, we use the theory of value distribution to study the uniqueness problems of two meromorphic functions and the relation of two meromorphic functions satisfying some functional equations. Also we prove some uniqueness results on two meromorphic functions with few poles sharing four small functions.
參考文獻 [1] R. Nevanlinna, Le th´eor"eme de Picard-Borel et la th´eorie des fonctions m´eromorphes, Gauthiers-Villars, Paris, 1929.
[2] H. Milloux, Les fonctions m´eromorphes et leurs d´eriv´ees, Paris, 1940.
[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 four values, Transactions of the American Mathematical Society, 277(2) (1983), 545–567.
[5] C. C. Yang and H. X. Yi, Uniqueness Theorem of Meromorphic Functions, Kluwer Academic Publishers, 2003.
[6] Q. D. Zhang, A uniqueness theorem for meromorphic functions with respect to solwly growing functions (Chinese), Acta Math. Sinica, 36 (1993), 826–833.
[7] Y. H. Li and J. Y. Qiao, On the uniqueness of meromorphic functions concerning small functions (Chinese), Preprint 1998.
[8] K. Ishizaki, Meromorphic functions sharing small functions, Acta Math. 77 (2001), 273–277.
[9] K. Ishizaki, Uniqueness problems on meromorphic functions that share four small functions, Proceedings of Second ISAAC Congress, Kluwer (2000), 467–472.
[10] P. Li, Meromorphic functions that share four small functions, J. Math. Anal. Appl, 263 (2001), 316–326.
[11] K. Ishizaki and N. Toda, Unicuty theorem for meromorphic functions with a few poles sharing four small meromorphic functions, Kodai Math. J. 21 (1998), 350–371.
[12] C. T. Chuang and C. C. Yang, Fixed points and factorization theory of meromorphic functions, Peking Univ. Press, 1988.
[13] F. Gross, Factorizatioin of meromorphic functions, U. S. Government Printing Office, Washington, D. C.,1972.
[14] W. K. Hayman, Meromorphic functions, Clarendon Press, Oxford, 1964.
[15] C. C. Yang and H. X. Yi, Uniqueness theory of meromorphic functions, Pure and Applied Math. Monographs No. 32, Science Press, Beijing, 1995.
[16] L. Yang, Value distribution theory, Berlin Heidelberg: Springer-Verlag, Beijing: Science Press, 1993.
描述 碩士
國立政治大學
應用數學研究所
95751003
97
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0095751003
資料類型 thesis
dc.contributor.advisor 陳天進zh_TW
dc.contributor.author (作者) 郭玲伶zh_TW
dc.creator (作者) 郭玲伶zh_TW
dc.date (日期) 2008en_US
dc.date.accessioned 8-十二月-2010 11:46:52 (UTC+8)-
dc.date.available 8-十二月-2010 11:46:52 (UTC+8)-
dc.date.issued (上傳時間) 8-十二月-2010 11:46:52 (UTC+8)-
dc.identifier (其他 識別碼) G0095751003en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/49453-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學研究所zh_TW
dc.description (描述) 95751003zh_TW
dc.description (描述) 97zh_TW
dc.description.abstract (摘要) 在這篇論文裡，我們利用值分佈理論來探討兩個半純函數何時會相等，進而了解兩個半純函數滿足某一函數方程時，其關係為何。最後，我們探討兩個半純函數共四個少函數且擁有少量的極點之相關性質。zh_TW
dc.description.abstract (摘要) In this thesis, we use the theory of value distribution to study the uniqueness problems of two meromorphic functions and the relation of two meromorphic functions satisfying some functional equations. Also we prove some uniqueness results on two meromorphic functions with few poles sharing four small functions.en_US
dc.description.tableofcontents 謝辭 i
Abstract ii
中文摘要 iii
Introduction 1
Basic Theory of Value Distribution 2
Rational Functions Sharing Values 13
Meromorphic Functions satisfying some Functional Equations 14
Meromorphic Functions with Few Poles 27
References 44		zh_TW
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dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0095751003en_US
dc.subject (關鍵詞) 半純函數zh_TW
dc.subject (關鍵詞) 唯一性zh_TW
dc.subject (關鍵詞) 少函數zh_TW
dc.subject (關鍵詞) meromorphic functionsen_US
dc.subject (關鍵詞) uniquenessen_US
dc.subject (關鍵詞) small functionen_US
dc.title (題名) 半純函數共慢成長函數之唯一性zh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] R. Nevanlinna, Le th´eor"eme de Picard-Borel et la th´eorie des fonctions m´eromorphes, Gauthiers-Villars, Paris, 1929.zh_TW
dc.relation.reference (參考文獻) [2] H. Milloux, Les fonctions m´eromorphes et leurs d´eriv´ees, Paris, 1940.zh_TW
dc.relation.reference (參考文獻) [3] G. G. Gundersen, Meromorphic functions that share three or four values, J. London Math. Soc., 20 (1979), 457–466.zh_TW
dc.relation.reference (參考文獻) [4] G. G. Gundersen, Meromorphic functions that share four values, Transactions of the American Mathematical Society, 277(2) (1983), 545–567.zh_TW
dc.relation.reference (參考文獻) [5] C. C. Yang and H. X. Yi, Uniqueness Theorem of Meromorphic Functions, Kluwer Academic Publishers, 2003.zh_TW
dc.relation.reference (參考文獻) [6] Q. D. Zhang, A uniqueness theorem for meromorphic functions with respect to solwly growing functions (Chinese), Acta Math. Sinica, 36 (1993), 826–833.zh_TW
dc.relation.reference (參考文獻) [7] Y. H. Li and J. Y. Qiao, On the uniqueness of meromorphic functions concerning small functions (Chinese), Preprint 1998.zh_TW
dc.relation.reference (參考文獻) [8] K. Ishizaki, Meromorphic functions sharing small functions, Acta Math. 77 (2001), 273–277.zh_TW
dc.relation.reference (參考文獻) [9] K. Ishizaki, Uniqueness problems on meromorphic functions that share four small functions, Proceedings of Second ISAAC Congress, Kluwer (2000), 467–472.zh_TW
dc.relation.reference (參考文獻) [10] P. Li, Meromorphic functions that share four small functions, J. Math. Anal. Appl, 263 (2001), 316–326.zh_TW
dc.relation.reference (參考文獻) [11] K. Ishizaki and N. Toda, Unicuty theorem for meromorphic functions with a few poles sharing four small meromorphic functions, Kodai Math. J. 21 (1998), 350–371.zh_TW
dc.relation.reference (參考文獻) [12] C. T. Chuang and C. C. Yang, Fixed points and factorization theory of meromorphic functions, Peking Univ. Press, 1988.zh_TW
dc.relation.reference (參考文獻) [13] F. Gross, Factorizatioin of meromorphic functions, U. S. Government Printing Office, Washington, D. C.,1972.zh_TW
dc.relation.reference (參考文獻) [14] W. K. Hayman, Meromorphic functions, Clarendon Press, Oxford, 1964.zh_TW
dc.relation.reference (參考文獻) [15] C. C. Yang and H. X. Yi, Uniqueness theory of meromorphic functions, Pure and Applied Math. Monographs No. 32, Science Press, Beijing, 1995.zh_TW
dc.relation.reference (參考文獻) [16] L. Yang, Value distribution theory, Berlin Heidelberg: Springer-Verlag, Beijing: Science Press, 1993.zh_TW