Ruelle zeta functions for finite dynamical systems and Koyama-Nakajima’s \(L\)-functions. (English) Zbl 1412.11117

Summary: A complex reflection determines an \(L\)-function which is a generalization of the Artin-Mazur zeta function associated with an element of the symmetric group. The present paper shows that the \(L\)-function is the Ruelle zeta function associated with a weighted \(\mathbf{Z}\)-dynamical system.


11M41 Other Dirichlet series and zeta functions
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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