Siegel-Klingen Theorem

Theorem (Siegel-Klingen Theorem, [1],[2]).

Let $K$ be a totally real number field and let $\zeta \mathit{}\mathrm{(}s\mathrm{,}K\mathrm{)}$ be the Dedekind zeta function of $K$. If $n\mathrm{\ge }\mathrm{1}$ is an integer then $\zeta \mathit{}\mathrm{(}\mathrm{-}n\mathrm{,}K\mathrm{)}$ is a rational number (i.e. $\zeta \mathit{}\mathrm{(}\mathrm{-}n\mathrm{,}K\mathrm{)}\mathrm{\in }\mathrm{Q}$).