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Annals of Mathematics
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arXiv.org e-Print Archive
Preprint . 2016
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Annals of Mathematics
Article . 2017 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2016
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The sphere packing problem in dimension $8$

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 May 2017Embargo end date: 01 Jan 2016Publisher:Annals of MathematicsJournal:Annals of Mathematics, volume 185 (issn: 0003-486X, Copyright policy )
Authors: Maryna Viazovska;

doi: 10.4007/annals.2017.185.3.7 , 10.48550/arxiv.1603.04246

arXiv: http://arxiv.org/abs/1603.04246

The sphere packing problem in dimension $8$

Abstract

In this paper we prove that no packing of unit balls in Euclidean space $\mathbb{R}^8$ has density greater than that of the $E_8$-lattice packing.

22 pages, 2 figures

Keywords

Mathematics - Number Theory, Mathematics - Metric Geometry, FOS: Mathematics, Metric Geometry (math.MG), Number Theory (math.NT)

  • BIP!
    Impact byBIP!
    citations
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 207
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Top 1%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Top 1%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    		 Top 1%
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
207
Top 1%
Top 1%
Top 1%
Green
bronze