Examples
- For the field of rational numbers, the idele class group is isomorphic to the product of the positive reals with all the unit groups of the p-adic integers. So a quasicharacter can be written as product of a power of the norm with a Dirichlet character.
- A Hecke character χ of the Gaussian integers of conductor 1 is of the form
- χ((a)) = |a|s(a/|a|)4n
- for s imaginary and n an integer, where a is a generator of the ideal (a). The only units are powers of i, so the factor of 4 in the exponent ensures that the character is well defined on ideals.
Read more about this topic: Hecke Character
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