Hecke character

Summary

A Hecke character of a number field $K$ is a continuous homomorphism from the idele class group $C_K$ to the nonzero complex numbers. Hecke characters generalize Dirichlet characters, which are the Hecke characters of finite order of $\Q$. Each Hecke character has an L-function with an Euler product, a meromorphic continuation and a functional equation, proved by Hecke and again by Tate's thesis.