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：
\[\sum_{j=1}^pa_j(z)f_j(z)^{k_j}=1,\]
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:
\[\sum_{j=1}^pa_j(z)f_j(z)^{k_j}=1,\]
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.
| Identifer | oai:union.ndltd.org:CHENGCHI/G0097751003 |
| Creators | 葉長青, Yeh, Chang Ching |
| Publisher | 國立政治大學 |
| Source Sets | National Chengchi University Libraries |
| Language | 英文 |
| Detected Language | English |
| Type | text |
| Rights | Copyright © nccu library on behalf of the copyright holders |
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