nLab
class number

Contents

Definition

In number theory, the class number of a number field is the order of its ideal class group.

Properties

Relation to the pole of the zeta function

The Dedekind zeta function ζ K\zeta_K of KK has a simple pole at s=1s = 1. The class number formula says that its residue there is proportional the the product of the regulator with the class number of KK

lims1(s1)ζ K(s)ClassNumber KRegulator K. \underset{s\to 1}{\lim} (s-1) \zeta_K(s) \propto ClassNumber_K \cdot Regulator_K \,.

References

Created on August 25, 2014 at 23:50:23. See the history of this page for a list of all contributions to it.