Counterexamples to a conjecture of Woods

Oded Regev; Uri Shapira; Barak Weiss

doi:10.1215/00127094-2017-0018

Abstract

A conjecture of Woods from 1972 is disproved: for $d\geq30$ , there are well-rounded unimodular lattices in ${\mathbb{R}}^{d}$ with covering radius greater than that of ${\mathbb{Z}}^{d}$ .

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Oded Regev. Uri Shapira. Barak Weiss. "Counterexamples to a conjecture of Woods." Duke Math. J. 166 (13) 2443 - 2446, 15 September 2017. https://doi.org/10.1215/00127094-2017-0018

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Received: 16 May 2016; Revised: 2 December 2016; Published: 15 September 2017

First available in Project Euclid: 9 June 2017

zbMATH: 1380.11086

MathSciNet: MR3703433

Digital Object Identifier: 10.1215/00127094-2017-0018

Subjects:

Primary: 11H31

Secondary: 11H06

Keywords: conjecture of Woods , covering radius , stable lattices

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