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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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