Completed Epstein zeta function
= Completed Epstein zeta function
{title2=$\mathcal E_\Lambda(s)=\pi^{-s}\Gamma(s)E_\Lambda(s)$}
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.