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
 |
where 
is a Legendre symbol, which is equivalent to the
Euler L-function. The definition over arbitrary
polynomials generalizes the above expression.
