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Remarks on the zeta function of a graph

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  • We make two observations about the zeta function of a graph. First we show how Bass’s proof of Ihara’s formula fits into the framework of torsion of complexes. Second, we show how in the special case of those graphs that are quotients of the Bruhat-Tits tree for SL(2, $K$) for a local nonarchimedean field $K$, the zeta function has a natural expression in terms of the $L$-functions of Coexter systems.
    Mathematics Subject Classification: Primary: 11M41, Secondary: 11F72, 14G35, 20E42.


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