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Lin and Wang defined a model of random walks on knot diagrams and interpretethe Alexnader polynomials and the colored Jones polynomials as Ihara zetafunctions, i.e. zeta functions defined by counting cycles on the knot diagram.Using this explanation, they gave a more conceptual proof for the Melvin-Mortonconjecture. In this paper, we give an analogous zeta function expression forthe twisted Alexander invariants.

Ihara zeta function and twisted Alexander invariants