TY - JOUR
T1 - Artin L-Functions on Finite Quotients of PGL3
AU - Kang, Ming Hsuan
AU - Winnie Li, Wen Ching
N1 - Publisher Copyright:
© 2014 The Author(s) 2014. Published by Oxford University Press. All rights reserved.
PY - 2015
Y1 - 2015
N2 - Let XΓ be a finite 2D complex arising from PGL3. In this paper, we study Artin L-functions attached to finite-dimensional representations ρ of the fundamental group of XΓ. 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 ρ, generalizing the identity on zeta functions of XΓ obtained in [9, 10].
AB - Let XΓ be a finite 2D complex arising from PGL3. In this paper, we study Artin L-functions attached to finite-dimensional representations ρ of the fundamental group of XΓ. 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 ρ, generalizing the identity on zeta functions of XΓ obtained in [9, 10].
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U2 - 10.1093/imrn/rnu215
DO - 10.1093/imrn/rnu215
M3 - Article
AN - SCOPUS:84950319810
SN - 1073-7928
VL - 2015
SP - 9251
EP - 9276
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 19
ER -