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- W4299281808 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." @default.
- W4299281808 created "2022-10-02" @default.
- W4299281808 creator A5025375824 @default.
- W4299281808 date "2021-07-10" @default.
- W4299281808 modified "2023-10-14" @default.
- W4299281808 title "Lattice packings through division algebras" @default.
- W4299281808 doi "https://doi.org/10.48550/arxiv.2107.04844" @default.
- W4299281808 hasPublicationYear "2021" @default.
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