Browsing by Author "Wang, Chian-Jen"

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Zeta and L-functions of finite quotients of apartments and buildings
(2018-10-01)
Kang, Ming-Hsuan
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Li, Wen-Ching Winnie
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Wang, Chian-Jen
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應用數學系
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Department of Applied Mathematics
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.