Zeta Functions of Complexes Arising from PGL(3)

Abstract

In this paper we obtain a closed form expression of the zeta function $Z(X_{\Gamma },u)$ of a finite quotient $X_{\Gamma }=\Gamma \backslash PG{L}_3(F)/PG{L}_3(O_F)$ of the Bruhat-Tits building of $PG{L}_3$ over a nonarchimedean local field $F$. Analogous to a graph zeta function, $Z(X_{\Gamma },u)$ is a rational function and it satisfies the Riemann hypothesis if and only if $X_{\Gamma }$ is a Ramanujan complex.

References in corpus (2)

• The Ihara-Selberg zeta function for PGL(3) and Hecke operators
• Lefschetz formulae and zeta functions

Cited by in corpus (2)

• Cutoff on Ramanujan complexes and classical groups
• Zeta Functions of F1-buildings