American Institute of Mathematical Sciences

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2003, 2003(Special): 413-422. doi: 10.3934/proc.2003.2003.413

Remarks on the zeta function of a graph

J. William Hoffman 1,

1. 

Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803, United States

Received  September 2002 Revised  February 2003 Published  April 2003

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.
Keywords: Keywords and Phrases.
Mathematics Subject Classification: Primary: 11M41, Secondary: 11F72, 14G35, 20E4.
Citation: J. William Hoffman. Remarks on the zeta function of a graph. Conference Publications, 2003, 2003 (Special) : 413-422. doi: 10.3934/proc.2003.2003.413
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