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 |
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Pages (from-to) | 46-103 |
Number of pages | 58 |
Journal | Advances in Mathematics |
Volume | 256 |
DOIs | |
State | Published - 1 May 2014 |
Keywords
- Bruhat-Tits building
- Discrete cocompact subgroups
- Primary
- Secondary
- Zeta functions