A New Determinant Expression for the Weighted Bartholdi Zeta Function of a Digraph

Iwao Sato, Hideo Mitsuhasi, Hideaki Morita

Abstract


We 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.

Keywords


zeta function, digraph, covering, $L$-function

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