Zeta functions of complexes arising from PGL(3)

Ming-Hsuan Kang; Wen Ching Winnie Li

doi:10.1016/j.aim.2013.12.033

Zeta functions of complexes arising from PGL(3)

Ming-Hsuan Kang^*, Wen Ching Winnie Li

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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.

Original language	English
Pages (from-to)	46-103
Number of pages	58
Journal	Advances in Mathematics
Volume	256
DOIs	https://doi.org/10.1016/j.aim.2013.12.033
State	Published - 1 May 2014

Keywords

Bruhat-Tits building
Discrete cocompact subgroups
Primary
Secondary
Zeta functions

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