DOI: 10.1017/fmp.2026.10040 ISSN: 2050-5086

A variational principle for Gaussian lattice sums

Laurent Bétermin, Markus Faulhuber, Stefan Steinerberger
Show PDF Cite

Abstract

We consider a two-dimensional analog of Jacobi theta functions and prove that, among all lattices

Λ ⊂ R 2 $\Lambda \subset \mathbb {R}^2$ normal upper Lamda subset of double struck upper R squared
with fixed density, the minimal value is maximized by the hexagonal lattice. This result can be seen as the inhomogeneous counterpart to Montgomery’s 1988 result, which proved that the hexagonal lattice minimizes the maximum.

More from our Archive