Browsing by Author "Li, Wen-Ching Winnie"

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Artin L-Functions on Finite Quotients of PGL(3)
(2015-01-01)
Kang, Ming-Hsuan
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Li, Wen-Ching Winnie
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應用數學系
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Department of Applied Mathematics
Let XG be a finite 2D complex arising from PGL3. In this paper, we study Artin Lfunctions attached to finite- dimensional representations. of the fundamental group of XG. Some key properties, including rationality, functional equation, and invariance under induction, of these functions are proved. Moreover, using a cohomological argument, we establish a connection between the Artin L- functions and the L- function of., generalizing the identity on zeta functions of XG obtained in [ 9, 10].
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.
Zeta functions of complexes arising from PGL(3)
(2014-05-01)
Kang, Ming-Hsuan
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Li, Wen-Ching Winnie
;
應用數學系
;
Department of Applied Mathematics
In this paper we obtain a closed form expression of the zeta function Z(Xr,u) of a finite quotient Xr of the Bruhat-Tits building of PGL(3) over a nonarchimedean local field F by a discrete cocompact torsion-free subgroup Gamma of PGL3. Analogous to a graph zeta function, Z(Xr, u) is a rational function with two different expressions and it satisfies the Riemann hypothesis if and only if Xr is a Ramanujan complex. (C) 2014 Elsevier Inc. All rights reserved.