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

$\underset{s\to 1}{\lim} (s-1) \zeta_K(s) \propto ClassNumber_K \cdot Regulator_K \,.$

## References

Created on August 25, 2014 at 23:46:13. See the history of this page for a list of all contributions to it.