We define a weighted alternating zeta function of a digraph D and give its determinant expression. We present a decomposition formula for the weighted alternating zeta function of a group covering of D. Furthermore, we introduce a weighted alternating L-function of D and present a determinant expression of it. As a corollary, we present a decomposition formula for the weighted alternating zeta function of a group covering of D by its weighted alternating L-functions.

中文翻译：

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有向图的加权交替 zeta 函数

我们定义有向图D的加权交替 zeta 函数并给出其行列式表达式。我们提出了D的群覆盖的加权交替 zeta 函数的分解公式。此外，我们引入了D的加权交替L函数并给出了它的行列式表达式。作为推论，我们通过其加权交替L函数提出了D的群覆盖的加权交替 zeta 函数的分解公式。