= Lattice theta functional equation
{title2=$\Theta_\Lambda(\tau)=(-i\tau)^{-n/2}m(\Lambda)^{-1}\Theta_{\Lambda^\vee}(-1/\tau)$}
For a full-rank <Euclidean lattice>, $\Theta_\Lambda(\tau)=\sum_{x\in\Lambda}e^{\pi i|x|^2\tau}$ obeys $\Theta_\Lambda(\tau)=(-i\tau)^{-n/2}m(\Lambda)^{-1}\Theta_{\Lambda^\vee}(-1/\tau)$. Apply the <Poisson summation formula for a Euclidean lattice> and the <complex Gaussian Fourier transform>. The identity holds without assuming an integral or self-dual lattice.
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