Abstract
We obtain new upper bounds on the minimal density of lattice coverings of by dilates of a convex body. We also obtain bounds on the probability (with respect to the natural Haar-Siegel measure on the space of lattices) that a randomly chosen lattice satisfies. As a step in the proof, we utilize and strengthen results on the discrete Kakeya problem.
Original language | English (US) |
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Pages (from-to) | 295-308 |
Number of pages | 14 |
Journal | Journal of the American Mathematical Society |
Volume | 35 |
Issue number | 1 |
DOIs | |
State | Published - 2022 |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics