Zeta Functions of Complexes Arising from PGL(3)

In this paper we obtain a closed form expression of the zeta function $Z(X_Γ, u)$ of a finite quotient $X_Γ= Γ\backslash PGL_3(F)/PGL_3(O_F)$ of the Bruhat-Tits building of $PGL_3$ over a nonarchimedean local field $F$. Analogous to a graph zeta function, $Z(X_Γ, u)$ is a rational function and it satisfies the Riemann hypothesis if and only if $X_Γ$ is a Ramanujan complex.

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