= Gaussian dyadic summation bound
{c}
{title2=$\sum_{j\ge0}e^{\varepsilon jh-c(jh)^2/L}\ll_{c,h}\sqrt L\,e^{\varepsilon^2L/(4c)}$}
For fixed $c,h>0$, $L\ge1$ and $\varepsilon\ge0$, complete the square in the exponent. A translated <Gaussian function> summed on a fixed-spaced lattice has mass $O(\sqrt L)$ uniformly in the translate, by comparison with its integral and its maximum. This keeps a square-root logarithm, rather than the full number of dyadic intervals, when summing exponentially damped <exponential sum> bounds.
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