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Ruelle zeta functions for finite digraphs. (English) Zbl 1446.05039

Summary: Three types of expressions for combinatorial zeta functions are considered. We investigate conditions for reformulating the exponential expression to the Euler product expression, and the Euler product expression to the determinant expression of Hashimoto type. The existence of the determinant expression of Hashimoto type enables to unify those zetas within a single framework, that is, the Ruelle zeta functions for quasi-finite dynamical systems constructed on finite digraphs, which we call the combinatorial zeta functions.

MSC:

05C20 Directed graphs (digraphs), tournaments
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
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