 Completed Epstein zeta function

The completion ${\mathcal{E}}_{\Lambda }(s)={\pi }^{-s}\Gamma (s)E_{\Lambda }(s)$ satisfies ${\mathcal{E}}_{\Lambda }(s)=m(\Lambda {)}^{-1}{\mathcal{E}}_{{\Lambda }^{\vee }}(n/2-s)$. Its simple poles at zero and $n/2$ have residues $-1$ and $m(\Lambda {)}^{-1}$. The pole-subtracted theta integral for an Epstein zeta function gives both the continuation and this dual lattice symmetry.