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

Ming-Hsuan Kang*, Wen Ching Winnie Li, Chian Jen Wang

*Corresponding author for this work

研究成果: Article同行評審

2 引文 斯高帕斯(Scopus)

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 =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.

原文English
頁(從 - 到)79-117
頁數39
期刊Israel Journal of Mathematics
228
發行號1
DOIs
出版狀態Published - 1 十月 2018

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