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題名 A 類半純函數之某些值分佈
Some value distribution of Meromorphic functions of Class A
作者 陳盈穎
Chen, Ying Ying
貢獻者 陳天進
Chen, Ten Ging
陳盈穎
Chen, Ying Ying
關鍵詞 值分佈理論
半純函數
A類半純函數
Value Distribution Theory
Meromorphic Function
Meromorphic Function of Class A
日期 2011
上傳時間 17-Apr-2012 10:27:45 (UTC+8)
摘要 在這篇論文裡，我們探討 $\\mathcal{A}$ 類半純函數的值分佈基本理論。我們證明了每一個 $\\mathcal{A}$ 類半純函數最多有兩個重值，而這個結果是最佳的情形。進而，我們證明若一個 $\\mathcal{A}$ 類半純函數 $f$ 與其導數 $f^{(k)}$ 共非零的複數值，則 $f\\equiv f^{(k)}$。
In this thesis, we study the basic theory of value distribution of meromorphic function of class $\\mathcal{A}$. We prove that every meromorphic function of class $\\mathcal{A}$ has at most two multiple values and the result is sharp. Also, we prove that if a meromorphic function $f$ of class $\\mathcal{A}$ and its derivative $f^{(k)}$ share a non-zero complex value, then $f\\equiv f^{(k)}$.
參考文獻 [1] C.-T. Chuang and C.-C. Yang, Fix-points and factorization of meromorphic functions, World Scienti c Publishing Co. Inc., Teaneck, NJ, 1990. Translated from the Chinese.
[2] G. Frank and G. Wei enborn, Meromorphe Funktionen, die mit einer ihrer Ableitungen Werte teilen, Complex Variables Theory Appl., 7 (1986), pp. 33{43.
[3] F. Gross, Factorization of meromorphic functions, Mathematics Research Center, Naval Research Laboratory, Washington, D. C., 1972.
[4] G. G. Gundersen, Meromorphic functions that share three or four values, J. London Math. Soc. (2), 20 (1979), pp. 457{466.
[5] , Meromorphic functions that share four values, Trans. Amer. Math. Soc., 277 (1983), pp. 545{567.
[6] W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964.
[7] H. Milloux, Les fonctions m eromorphes et leurs d eriv ees. Extensions d`un th eor eme de M. R. Nevanlinna. Applications, Actualit es Sci. Ind., no. 888, Hermann et Cie., Paris, 1940.
[8] R. Nevanlinna, Le th eor eme de Picard-Borel et la th eorie des fonctions m eromorphes, Chelsea Publishing Co., New York, 1974. Reprinting of the 1929 original.
[9] C.-C. Yang and H.-X. Yi, Uniqueness theory of meromorphic functions, vol. 557 of Mathematics and its Applications, Kluwer Academic Publishers Group, Dordrecht, 2003.
[10] L. Yang, Value distribution theory, Springer-Verlag, Berlin, 1993. Translated and revised from the 1982 Chinese original.
描述 碩士
國立政治大學
應用數學研究所
98751003
100
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0987510031
資料類型 thesis
dc.contributor.advisor 陳天進zh_TW
dc.contributor.advisor Chen, Ten Gingen_US
dc.contributor.author (Authors) 陳盈穎zh_TW
dc.contributor.author (Authors) Chen, Ying Yingen_US
dc.creator (作者) 陳盈穎zh_TW
dc.creator (作者) Chen, Ying Yingen_US
dc.date (日期) 2011en_US
dc.date.accessioned 17-Apr-2012 10:27:45 (UTC+8)-
dc.date.available 17-Apr-2012 10:27:45 (UTC+8)-
dc.date.issued (上傳時間) 17-Apr-2012 10:27:45 (UTC+8)-
dc.identifier (Other Identifiers) G0987510031en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/52850-
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) 98751003zh_TW
dc.description (描述) 100zh_TW
dc.description.abstract (摘要) 在這篇論文裡，我們探討 $\\mathcal{A}$ 類半純函數的值分佈基本理論。我們證明了每一個 $\\mathcal{A}$ 類半純函數最多有兩個重值，而這個結果是最佳的情形。進而，我們證明若一個 $\\mathcal{A}$ 類半純函數 $f$ 與其導數 $f^{(k)}$ 共非零的複數值，則 $f\\equiv f^{(k)}$。zh_TW
dc.description.abstract (摘要) In this thesis, we study the basic theory of value distribution of meromorphic function of class $\\mathcal{A}$. We prove that every meromorphic function of class $\\mathcal{A}$ has at most two multiple values and the result is sharp. Also, we prove that if a meromorphic function $f$ of class $\\mathcal{A}$ and its derivative $f^{(k)}$ share a non-zero complex value, then $f\\equiv f^{(k)}$.en_US
dc.description.tableofcontents 謝辭­ .......................... i
Abstract ­ .......................... iii
中文摘要 ­ .......................... iv
Content ­ .......................... v
1 Introduction ­ .......................... 1
2 Basic Theory of Value Distribution ­ .......................... 3
3 Meromorphic Functions of Class A ­ .......................... 13
4 Multiple Values of Meromorphic Functions of Class A ­ .......................... 21
5 The Unicity of Meromorphic Functions of Class A ­ .......................... 24
References ­ .......................... 27		zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0987510031en_US
dc.subject (關鍵詞) 值分佈理論zh_TW
dc.subject (關鍵詞) 半純函數zh_TW
dc.subject (關鍵詞) A類半純函數zh_TW
dc.subject (關鍵詞) Value Distribution Theoryen_US
dc.subject (關鍵詞) Meromorphic Functionen_US
dc.subject (關鍵詞) Meromorphic Function of Class Aen_US
dc.title (題名) A 類半純函數之某些值分佈zh_TW
dc.title (題名) Some value distribution of Meromorphic functions of Class Aen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] C.-T. Chuang and C.-C. Yang, Fix-points and factorization of meromorphic functions, World Scienti c Publishing Co. Inc., Teaneck, NJ, 1990. Translated from the Chinese.zh_TW
dc.relation.reference (參考文獻) [2] G. Frank and G. Wei enborn, Meromorphe Funktionen, die mit einer ihrer Ableitungen Werte teilen, Complex Variables Theory Appl., 7 (1986), pp. 33{43.zh_TW
dc.relation.reference (參考文獻) [3] F. Gross, Factorization of meromorphic functions, Mathematics Research Center, Naval Research Laboratory, Washington, D. C., 1972.zh_TW
dc.relation.reference (參考文獻) [4] G. G. Gundersen, Meromorphic functions that share three or four values, J. London Math. Soc. (2), 20 (1979), pp. 457{466.zh_TW
dc.relation.reference (參考文獻) [5] , Meromorphic functions that share four values, Trans. Amer. Math. Soc., 277 (1983), pp. 545{567.zh_TW
dc.relation.reference (參考文獻) [6] W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964.zh_TW
dc.relation.reference (參考文獻) [7] H. Milloux, Les fonctions m eromorphes et leurs d eriv ees. Extensions d`un th eor eme de M. R. Nevanlinna. Applications, Actualit es Sci. Ind., no. 888, Hermann et Cie., Paris, 1940.zh_TW
dc.relation.reference (參考文獻) [8] R. Nevanlinna, Le th eor eme de Picard-Borel et la th eorie des fonctions m eromorphes, Chelsea Publishing Co., New York, 1974. Reprinting of the 1929 original.zh_TW
dc.relation.reference (參考文獻) [9] C.-C. Yang and H.-X. Yi, Uniqueness theory of meromorphic functions, vol. 557 of Mathematics and its Applications, Kluwer Academic Publishers Group, Dordrecht, 2003.zh_TW
dc.relation.reference (參考文獻) [10] L. Yang, Value distribution theory, Springer-Verlag, Berlin, 1993. Translated and revised from the 1982 Chinese original.zh_TW