半純函數體中的函數方程

• Main Authors: 葉長青, Yeh, Chang Ching
• Language: 英文
• Published: 國立政治大學
• Subjects: 半純函數; 值分佈理論; 函數方程; meromorphic function; value distribution theory; functional equation
• Online Access: http://thesis.lib.nccu.edu.tw/cgi-bin/cdrfb3/gsweb.cgi?o=dstdcdr&i=sid=%22G0097751003%22.

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.