class number formula

Given a number field $K$, 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 product of the regulator with the class number of $K$

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

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

- Wikipedia,
*Class number formula*

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