A New Determinant Expression for the Weighted Bartholdi Zeta Function of a Digraph
Keywords: zeta function, digraph, covering, $L$-function
AbstractWe consider the weighted Bartholdi zeta function of a digraph $D$, and give a new determinant expression of it. Furthermore, we treat a weighted $L$-function of $D$, and give a new determinant expression of it. As a corollary, we present determinant expressions for the Bartholdi edge zeta functions of a graph and a digraph.