• Corpus ID: 238634561

A variational principle for Gaussian lattice sums

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