New bounds on the density of lattice coverings

Or Ordentlich; Oded Regev; Barak Weiss

doi:10.1090/jams/984

New bounds on the density of lattice coverings

Or Ordentlich, Oded Regev, Barak Weiss

The Hebrew University of Jerusalem, Tel Aviv University

Research output: Contribution to journal › Article › peer-review

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
Pages (from-to)	295-308
Number of pages	14
Journal	Journal of the American Mathematical Society
Volume	35
Issue number	1
DOIs	https://doi.org/10.1090/jams/984
State	Published - 1 Jan 2022

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/jams/984

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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.",

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AB - 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.

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New bounds on the density of lattice coverings

Abstract

All Science Journal Classification (ASJC) codes

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