Zeta and L-functions of finite quotients of apartments and buildings

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Title:	Zeta and L-functions of finite quotients of apartments and buildings
Authors:	Ming-Hsuan Kang;Wen-Ching Winnie Li;Chian-Jen Wang
Date:	2018-10
Issue Date:	2019-09-17 12:10:38 (UTC+8)
Publisher:	The Hebrew University Magnes Press
Abstract:	In this paper, we study relations between Langlands L-functions and zeta functions of geodesic walks and galleries for finite quotients of the apartments of G =PGL3 and PGSp4 over a nonarchimedean local field with q elements in its residue field. They give rise to an identity (Theorem 5.3) which can be regarded as a generalization of Ihara’s theorem for finite quotients of the Bruhat–Tits trees. This identity is shown to agree with the q = 1 version of the analogous identities for finite quotients of the building of G established in [KL14, KLW10, FLW13], verifying the philosophy of the field with one element by Tits. A new identity for finite quotients of the building of PGSp4 involving the standard L-function (Theorem 6.3), complementing the one in [FLW13] which involves the spin L-function, is also obtained.
Relation:	Israel Journal of Mathematics 228(1), p.79-117
DOI:	10.1007/s11856-018-1756-3
Appears in Collections:	[Graduate Institute & Department of Mathematics] Journal Article

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