Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 21 (2025), 019, 7 pages      arXiv:2501.05746      https://doi.org/10.3842/SIGMA.2025.019
Contribution to the Special Issue on Basic Hypergeometric Series Associated with Root Systems and Applications in honor of Stephen C. Milne

A Minimum Property for Cuboidal Lattice Sums

Shaun Cooper ^a and Peter Schwerdtfeger ^b
a) School of Mathematical and Computational Sciences, Massey University Albany, Private Bag 102904, North Shore Mail Centre, Auckland 0745, New Zealand
^b) Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study (NZIAS), Massey University Albany, Private Bag 102904, North Shore Mail Centre, Auckland 0745, New Zealand

Received January 13, 2025, in final form March 16, 2025; Published online March 24, 2025

Abstract
We analyse a family of lattices considered by Conway and Sloane and show that the corresponding Epstein zeta function attains a local minimum for the body-centred cubic lattice.

Key words: body-centred cubic; face-centred cubic; Epstein zeta function; lattice sum.

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