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We evaluate the classic sum $\sum_{n\in\mathbb{Z}} e^{-\pi n^2}$. The noveltyof our approach is that it does not require any prior knowledge about modularforms, elliptic functions or analytic continuations. Even the $\Gamma$function, in terms of which the result is expressed, only appears as a complexfunction in the computation of a real integral by the residue theorem. Anothercontribution of this note is to provide a very simple proof of the Kroneckerlimit formula.

A simple evaluation of a theta value and the Kronecker limit formula