nLab
class number formula

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Idea

Given a number field KK, 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 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 \,.

Variants of this for arithmetic varieties over \mathbb{Q} are the Birch and Swinnerton-Dyer conjecture and the Beilinson conjecture.

References

Last revised on August 27, 2014 at 07:13:22. See the history of this page for a list of all contributions to it.