@article{0e6b65c1e3e54306b6caae8b5cc6efaa,
title = "New bounds on the density of lattice coverings",
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.",
author = "Or Ordentlich and Oded Regev and Barak Weiss",
note = "Funding Information: Received by the editors June 11, 2020, and, in revised form, April 8, 2021. 2020 Mathematics Subject Classification. Primary 11H31, 94B75, 11T30. The authors were supported by grants ISF 2919/19, ISF 1791/17, BSF 2016256, the Simons Collaboration on Algorithms and Geometry, a Simons Investigator Award, and by the National Science Foundation (NSF) under Grant No. CCF-1814524. Publisher Copyright: {\textcopyright} 2021 American Mathematical Society.",
year = "2022",
doi = "10.1090/JAMS/984",
language = "English (US)",
volume = "35",
pages = "295--308",
journal = "Journal of the American Mathematical Society",
issn = "0894-0347",
publisher = "American Mathematical Society",
number = "1",
}