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Title: 半純函數體中的函數方程
On Functional Equations in the Field of Meromorphic Functions
Authors: 葉長青
Yeh, Chang Ching
Contributors: 陳天進
Chen, Ten Ging
Yeh, Chang Ching
Keywords: 半純函數
meromorphic function
value distribution theory
functional equation
Date: 2009
Issue Date: 2010-12-08 11:52:40 (UTC+8)
Abstract: 在這篇論文中,我們將利用值分佈的理論來探討下列函數方程解的存在性與其性質:
其中 $a_1(z),\cdots ,a_p(z)$ 為半純函數。對某些特殊方程,除了文獻裡已知的結果外,我們亦提供其它的例子。一般而言,我們探討解存在的必要條件。另外,我們證明了某一類半純函數之零點與極點之分佈的結果。
In this thesis, we use the theory of value distribution to study the existence of solution of the following functional equation:
where $a_1(z),\cdots ,a_p(z)$ are meromorphic functions. For some special case, new and old examples of the solutions are given. For the general case, a necessary condition for the existence of solution is considered. Moreover, we obtain a result on the distribution of zeros and poles of a class of meromorphic functions.
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Data Type: thesis
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