Dedekind zeta function

The Dedekind zeta function of a number field is defined as

Where the integral ideals of the number field passes and whose absolute norm. The series is absolutely and uniformly convergent in the field for all and it is

The prime ideals of passes. The zeta function has an analytic continuation.

The Dedekind zeta function thus represents a generalization of the Riemann zeta - function, which corresponds to the field of rational numbers.