Zeta functions of complexes arising from PGL(3)

Ming-Hsuan Kang*, Wen Ching Winnie Li

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


In this paper we obtain a closed form expression of the zeta function Z( , u) of a finite quotient 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( , u) is a rational function with two different expressions and it satisfies the Riemann hypothesis if and only if is a Ramanujan complex.

Original languageEnglish
Pages (from-to)46-103
Number of pages58
JournalAdvances in Mathematics
StatePublished - 1 May 2014


  • Bruhat-Tits building
  • Discrete cocompact subgroups
  • Primary
  • Secondary
  • Zeta functions

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