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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: 2012-04-17 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
    顯示於類別:[應用數學系] 學位論文

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