Artin L-Functions on Finite Quotients of PGL(3)

Abstract

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].