  In this paper we present an approach to study arithmetical properties of
global function fields by working with Artin L-functions. In particular we
recall and then extend a criteria of two function fields to be arithmetically
equivalent in terms of Artin L-functions of representations associated to the
common normal closure of those fields. We provide few examples of such
non-isomorphic fields and also discuss an algorithm to construct many such
examples by using torsion points on elliptic curves. Finally, we will show how
to apply our results in order to distinguish two global fields by a finite list
of Artin L-functions.
