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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AU - Kang, Ming-Hsuan

AU - Li, Wen Ching Winnie

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N2 - 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.

AB - 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.

KW - Bruhat-Tits building

KW - Discrete cocompact subgroups

KW - Primary

KW - Secondary

KW - Zeta functions

UR - http://www.scopus.com/inward/record.url?scp=84894284973&partnerID=8YFLogxK

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DO - 10.1016/j.aim.2013.12.033

M3 - Article

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SP - 46

EP - 103

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -

Zeta functions of complexes arising from PGL(3)

Abstract

Keywords

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