Lattice packings through division algebras
Number Theory
2021-09-28 v3 Metric Geometry
Abstract
In this article, we will show the existence of lattice packings in a sparse family of dimensions. This construction will be a generalisation of Venkatesh's lattice packing result. In our construction, we replace the appearance of the cyclotomic number field with a division algebra over the rational field. For this, we develop an analogue of Siegel's mean value theorem over lattices that have a prescribed set of symmetries given by a finite non-commutative group inside the multiplicative subgroup of a division algebra. This approach improves the best known lattice packing bounds in many dimensions.
Keywords
Cite
@article{arxiv.2107.04844,
title = {Lattice packings through division algebras},
author = {Nihar Prakash Gargava},
journal= {arXiv preprint arXiv:2107.04844},
year = {2021}
}