An Artin -function over the Rationals encodes in a Generating Function
information about how an irreducible monic Polynomial over factors when reduced modulo each Prime. For
the Polynomial , the Artin -function is
See also Langlands Reciprocity
Knapp, A. W. ``Group Representations and Harmonic Analysis, Part II.'' Not. Amer. Math. Soc. 43, 537-549, 1996.