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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
Chen, Ying Ying
Keywords: 值分佈理論
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 $f\equiv f^{(k)}$.
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[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.
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[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.
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[10] L. Yang, Value distribution theory, Springer-Verlag, Berlin, 1993. Translated and revised from the 1982 Chinese original.
Description: 碩士
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Data Type: thesis
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