Is there a Birch and Swinnerton-Dyer conjecture for Dedekind zeta functions?

Christopher Deninger

A Birch and Swinnerton-Dyer conjecture for number fields $K/\mathbb{Q}$ would assert that $dim{V}_K=or{d}_{s=1/2}{\zeta }_K(s)$ for some vector space functorially attached to $K$. Pr…