= Gaussian theta sum
{c}
{title2=$\theta_\Lambda(A)=\sum_{\lambda\in\Lambda}e^{-\pi\lambda^TA\lambda}$}
For a full <Euclidean lattice> $\Lambda$ and a positive definite real symmetric matrix $A$, the Gaussian theta sum is $\theta_\Lambda(A)=\sum_{\lambda\in\Lambda}e^{-\pi\lambda^TA\lambda}$. Its absolute convergence follows from Gaussian decay and the polynomial growth of the number of lattice points in a ball. The <Poisson summation formula for a Euclidean lattice> gives its <anisotropic theta functional equation>.
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