Maximal Theta Functions -- Universal Optimality of the Hexagonal Lattice for Madelung-Like Lattice Energies

2020/07/31 by Laurent Bétermin, Markus Faulhuber · 1 voice
Mathematics · Physics and Astronomy · #math.MG #math-ph #math.CA #math.NT

paper · pdf · doi:10.1007/s11854-022-0254-z

arxiv published 2020/07/31 · arxiv updated 2023/01/12

Abstract

We present two families of lattice theta functions accompanying the family of lattice theta functions studied by Montgomery in [H.~Montgomery. Minimal theta functions. Glasgow Mathematical Journal, 30(1):75--85, 1988]. The studied theta functions are generalizations of the Jacobi theta-2 and theta-4 functions. Contrary to Montgomery's result, we show that, among lattices, the hexagonal lattice is the unique maximizer of both families of theta functions. As an immediate consequence, we obtain a new universal optimality result for the hexagonal lattice among two-dimensional alternating charged lattices and lattices shifted by the center of their unit cell.

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• REPOST OF OLD TWEETS [15.11.2021] --- New paper on "Maximal Theta Functions — Universal Optimality of the Hexagonal Lattice for Madelung-Like Lattice Energies" by L. Bétermin and M. Faulhuber - accept [bsky, 0 points, 0 comments]

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