A unified simple proof of a conjecture of woods for n≤6

Hans-Gill, R. J. ; Raka, Madhu ; Sehmi, Ranjeet ; Sucheta, (2009) A unified simple proof of a conjecture of woods for n≤6 Journal of Number Theory, 129 (5). pp. 1000-1010. ISSN 0022-314X

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00223...

Related URL: http://dx.doi.org/10.1016/j.jnt.2008.10.021


Let Rn be the n-dimensional Euclidean space. Let L denote a lattice in Rn of determinant 1 such that there is a sphere centered at the origin O which contains n linearly independent points of L on its boundary but no point of L other than O inside it. A well-known conjecture in the geometry of numbers asserts that any closed sphere in Rn of radius ½√n contains a point of L. This is known to be true for n≤6. Here we give a unified simple proof for n≤6 of the more general conjecture of Woods.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Lattice; Sphere; Critical determinant; Non-homogeneous; Reduction
ID Code:12351
Deposited On:10 Nov 2010 06:25
Last Modified:03 Jun 2011 06:27

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