PreprintCC BY 4.0arXiv
A cyclotomic gluing construction for lattice sphere packings
Abstract
For a positive integer d, let ΔdL denote the supremum of the densities of lattice sphere packings in ℝd. We prove that, for every sufficiently large d, ΔdL ≫ d2loglog d 2−d. Abuya-Gargava-Zhao obtained the same bound along a sparse sequence of dimensions by combining Venkatesh's cyclotomic symmetries with Klartag's stochastic ellipsoid method. We introduce a multi-cyclotomic gluing construction that allows this argument to work in every sufficiently large dimension.
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BibTeX
@misc{gargava2026cyclotomic,
title = {{A cyclotomic gluing construction for lattice sphere packings}},
author = {Nihar Gargava and Matthias Gröbner and Michael Simkin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12619},
eprint = {2610.12619},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12619},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A cyclotomic gluing construction for lattice sphere packings
AU - Nihar Gargava
AU - Matthias Gröbner
AU - Michael Simkin
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12619
UR - https://arxiv.org/abs/2610.12619
AB - For a positive integer d, let Δ_d^L denote the supremum of the densities of lattice sphere packings in ℝ^d. We prove that, for every sufficiently large d, Δ_d^L ≫ d^2loglog d 2^−d. Abuya-Gargava-Zhao obtained the same bound along a sparse sequence of dimensions by combining Venkatesh's cyclotomic symmetries with Klartag's stochastic ellipsoid method. We introduce a multi-cyclotomic gluing construction that allows this argument to work in every sufficiently large dimension.
ER -