Remarks on the zeta function of a graph

Pages: 413 - 422, Issue Special, July 2003

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J. William Hoffman - Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803, United States (email)

Abstract: 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, 20E42.

Received: September 2002;      Revised: February 2003;      Published: April 2003.