Artin L-Functions on Finite Quotients of PGL₃

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].