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

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

Research output: Contribution to journalArticle

1 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)79-117
Number of pages39
JournalIsrael Journal of Mathematics
Volume228
Issue number1
DOIs
StatePublished - Oct 1 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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