A primitive 
-series
is a Dirichlet L-series 
whose number
theoretic character 
modulo 
is primitive. This means that its conductor equals 
, so it is not induced by a number
theoretic character of any proper divisor of 
.
If 
is induced by a primitive number theoretic
character 
of conductor 
dividing 
,
then
 |
Thus every imprimitive Dirichlet 
-series differs from a unique primitive one by finitely many
Euler factors. Primitive 
-series are therefore the basic factors in the decomposition
of Dirichlet 
-functions.
