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Title: A 類半純函數之某些值分佈
Some value distribution of Meromorphic functions of Class A
Authors: 陳盈穎
Chen, Ying Ying
Contributors: 陳天進
Chen, Ten Ging
陳盈穎
Chen, Ying Ying
Keywords: 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
Date: 2011
Issue Date: 2012-04-17 10:27:45 (UTC+8)
Abstract: 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 $f\equiv f^{(k)}$.
Reference: [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.
Description: 碩士
國立政治大學
應用數學研究所
98751003
100
Source URI: http://thesis.lib.nccu.edu.tw/record/#G0987510031
Data Type: thesis
Appears in Collections:[應用數學系] 學位論文

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