Work

A variational principle for Gaussian lattice sums

Year: 2026

Type: article

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.

Source: Forum of Mathematics Pi

DOI: 10.1017/fmp.2026.10040

Authors: Laurent Bétermin, Markus Faulhuber, Stefan Steinerberger

Institutions: Lyon 1 Université, University of Vienna, University of Washington

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,650

Funders: National Science Foundation, Alfred P. Sloan Foundation, Deutsche Forschungsgemeinschaft, Austrian Science Fund