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#dedekind_zeta_function

Dedekind zeta function

Generalization of the Riemann zeta function for algebraic number fields

In mathematics, the Dedekind zeta function of an algebraic number field K, generally denoted ζK(s), is a generalization of the Riemann zeta function (which is obtained in the case where K is the field of rational numbers Q). It can be defined as a Dirichlet series, it has an Euler product expansion, it satisfies a functional equation, it has an analytic continuation to a meromorphic function on the complex plane C with only a simple pole at s = 1, and its values encode arithmetic data of K. The extended Riemann hypothesis states that if ζK(s) = 0 and 0 < Re(s) < 1, then Re(s) = 1/2.

Sun 26th

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Dedekind zeta function List of zeta functions Riemann zeta function Arithmetic zeta function Dedekind function Class number formula Artin L-function Generalized Riemann hypothesis Dedekind psi function Riemann hypothesis

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