Dedekind zeta function
In mathematics, the Dedekind zeta function of an algebraic number field K, generally denoted , is a generalization of the Riemann zeta function that represents information of ideals in number ring in the similar way as Riemann zeta function represents information about integers.
Dedekind zeta functions generalize many properties of Riemann zeta function: they can be defined as a Dirichlet series, have an analytic continuation to a meromorphic function on the complex plane C with only a simple pole at s = 1, have an Euler product expansion, and satisfies a functional equation. Values of Dedekind zeta functions encode important arithmetic data of K.
The Dedekind zeta function is named for Richard Dedekind who introduced it in his supplement to Peter Gustav Lejeune Dirichlet's Vorlesungen über Zahlentheorie.