代数体函数与其系数函数的Borel点

研究了代数体函数的系数函数的Borel点与代数体函数的Borel点之间的关系. 先证明了定义在单位圆内的代数体函数的几个定理, 然后利用这些新定理证明了: $e^{it}$是单位圆内整代数体函数$W(z)$的$p(1)$级Borel点的充分必要条件是至少存在一个正整数$j\in\{0,1,2,...,k-1\}$,使$e^{it}$是系数函数$A_j(z)$的$p$级Borel点.

The Borel points of algebroidal function and its coefficient functions

The relationship between the Borel point of algebroid functions and that of its coefficient functions is studied in this paper. Some results on the algebroid function defined in the unit disc are established. As an application, $e^{it}$ is a Borel point of entire algebroid function $W (z) $ of order $p (>1) $ if and only if $e^{it}$ is a Borel point of coefficient function $A_j (z) $ of order $p$ for some positive integer $j\in\{0,1,2,..., k-1\}$ is proved.