On conjectures of Minkowski and Woods for \(n=7\)

DOI10.1016/j.jnt.2008.10.020zbMath1175.11033OpenAlexW2513602157WikidataQ123361680 ScholiaQ123361680MaRDI QIDQ1017385

Madhu Raka, Ranjeet Sehmi, R. J. Hans-Gill

Publication date: 19 May 2009

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2008.10.020

zbMATH Keywords

latticecoveringreductionnon-homogeneouscritical determinantproduct of linear forms

Mathematics Subject Classification ID

Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Lattice packing and covering (number-theoretic aspects) (11H31) Products of linear forms (11H46) Inhomogeneous linear forms (11J20)

Related Items (13)

Inhomogeneous minima of mixed signature lattices ⋮ On a question of Uri Shapira and Barak Weiss ⋮ On conjectures of Minkowski and Woods for \(n = 9\) ⋮ On conjectures of Minkowski and Woods for \(n=10\) ⋮ Upper bounds for the Euclidean minima of abelian fields of odd prime power conductor ⋮ Estimates on conjectures of Minkowski and Woods ⋮ A Generalization of a Result of Birch and Swinnerton-Dyer ⋮ Estimates on conjectures of Minkowski and Woods. II ⋮ Stable and well-rounded lattices in diagonal orbits ⋮ Upper bounds for the Euclidean minima of abelian fields ⋮ Stable lattices and the diagonal group ⋮ A unified simple proof of a conjecture of Woods for \(n\leq 6\) ⋮ Refined Estimates on Conjectures of Woods and Minkowski

Cites Work

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• A new variant of the proof of the inhomogeneous Minkowski conjecture for n=5
• Upper bounds for Euclidean minima of algebraic number fields
• Minkowski's conjecture for \(n=5\); a theorem of Skubenko
• On a theorem of Dyson
• Representation of unimodular matrices in the form DOTU for n = 3
• The minimum values of positive quadratic forms in six, seven and eight variables
• Covering six space with spheres
• On the product of four non-homogeneous linear forms
• On the inhomogeneous minimum of the product of n linear forms
• Minkowski’s conjecture, well-rounded lattices and topological dimension
• Über einen Approximationssatz von Minkowski
• Convex and Discrete Geometry
• The densest double lattice packing of four‐spheres
• Lattice coverings of five space by spheres
• On Coverings of Four-Space by Spheres

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