標題: Zeta and L-functions of finite quotients of apartments and buildings
作者: Kang, Ming-Hsuan
Li, Wen-Ching Winnie
Wang, Chian-Jen
應用數學系
Department of Applied Mathematics
公開日期: 1-Oct-2018
摘要: 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 =PGL(3) and PGSp(4) 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 PGSp(4) involving the standard L-function (Theorem 6.3), complementing the one in [FLW13] which involves the spin L-function, is also obtained.
URI: http://dx.doi.org/10.1007/s11856-018-1756-3
http://hdl.handle.net/11536/148440
ISSN: 0021-2172
DOI: 10.1007/s11856-018-1756-3
期刊: ISRAEL JOURNAL OF MATHEMATICS
Volume: 228
起始頁: 79
結束頁: 117
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