# A variational principle for Gaussian lattice sums

@inproceedings{Betermin2021AVP, title={A variational principle for Gaussian lattice sums}, author={Laurent B'etermin and Markus Faulhuber and Stefan Steinerberger}, year={2021} }

We consider a two-dimensional analogue of Jacobi theta functions and prove that, among all lattices $\Lambda \subset \mathbb{R}^2$ with fixed density, the minimal value is maximized by the hexagonal lattice. This result can be interpreted as the dual of a 1988 result of Montgomery who proved that the hexagonal lattice minimizes the maximal values. Our inequality resolves a conjecture of Strohmer and Beaver about the operator norm of a certain type of frame in $L^2(\mathbb{R})$. It has…

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