[[Positive definite lattice]]
# Theta function of a lattice

Let $L$ be a [[positive definite lattice]].
The **theta function** $\vartheta_{L}$ of $L$ is the [[Formal sum|formal series]] #m/def/anal/comp  
$$
\begin{align*}
\vartheta_{L}(q) = \sum_{\alpha \in L} q^{\langle \alpha,\alpha \rangle / 2}= \sum_{m \in \mathbb{Q}} \abs{L_{m}} q^{m / 2}
\end{align*}
$$


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