Remarks on the zeta function of a graph

J. William Hoffman

doi:10.3934/proc.2003.2003.413

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2003, Volume 2003: 413-422. Doi: 10.3934/proc.2003.2003.413 open access

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Remarks on the zeta function of a graph

J. William Hoffman^1,

1.
Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803

Received: August 31, 2002

Revised: January 31, 2003

Published: March 2003

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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.

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Mathematics Subject Classification: Primary: 11M41, Secondary: 11F72, 14G35, 20E42.

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