Zeta functions of complexes arising from [formula omitted

Abstract

In this paper we obtain a closed form expression of the zeta function Z(XΓ,u) of a finite quotient XΓ of the Bruhat–Tits building of PGL3 over a nonarchimedean local field F by a discrete cocompact torsion-free subgroup Γ of PGL3. Analogous to a graph zeta function, Z(XΓ,u) is a rational function with two different expressions and it satisfies the Riemann hypothesis if and only if XΓ is a Ramanujan complex.