Primitive ray class characters #
A ray class character is primitive when it is not induced from any strictly smaller modulus. This formulation uses the transition maps of ray class groups and includes the real places in the conductor condition. In particular, the trivial character of a nontrivial modulus is imprimitive: it comes from the trivial modulus.
This is the finite-character distinction needed when assigning a least modulus to a Hecke character and when comparing ray class characters with Dirichlet characters.
References #
- J. Neukirch, Algebraic Number Theory, Chapter VI, ยง1.
A ray class character is primitive if it is not induced from a strictly smaller modulus.
Instances For
A character is primitive exactly when every modulus inducing it is its own modulus.
An imprimitive character is induced from a strictly smaller modulus.
A character induced from a strictly smaller modulus is imprimitive.
Every character of the trivial modulus is primitive.
The trivial character is primitive exactly at the trivial modulus.