New bounds on the density of lattice coverings

Or Ordentlich, Oded Regev, Barak Weiss

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 languageAmerican English
Pages (from-to)295-308
Number of pages14
JournalJournal of the American Mathematical Society
Volume35
Issue number1
DOIs
StatePublished - 2022

Bibliographical note

Publisher Copyright:
© 2021 American Mathematical Society.

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