TY - JOUR
T1 - Zeta functions of complexes arising from PGL(3)
AU - Kang, Ming Hsuan
AU - Li, Wen Ching Winnie
N1 - Funding Information:
This research was supported in part by the DARPA grant HR0011-06-1-0012 and the NSF grants DMS-0457574 and DMS-0801096 (both authors), NSF grant DMS-1101368 (W.-C.W. Li), and also the NSC grant 100-2115-M-009-008-MY2 (M. Kang). Part of the research was performed while both authors were visiting the National Center for Theoretical Sciences, Mathematics Division, in Hsinchu, Taiwan. They would like to thank the Center for its support and hospitality.
PY - 2014/5/1
Y1 - 2014/5/1
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.
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U2 - 10.1016/j.aim.2013.12.033
DO - 10.1016/j.aim.2013.12.033
M3 - Article
AN - SCOPUS:84894284973
SN - 0001-8708
VL - 256
SP - 46
EP - 103
JO - Advances in Mathematics
JF - Advances in Mathematics
ER -