Minkowski's conjecture for n = 5; a theorem of Skubenko

Bambah, R. P. ; Woods, A. C. (1980) Minkowski's conjecture for n = 5; a theorem of Skubenko Journal of Number Theory, 12 (1). pp. 27-48. ISSN 0022-314X

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Official URL: http://www.sciencedirect.com/science/article/pii/0...

Related URL: http://dx.doi.org/10.1016/0022-314X(80)90070-0

Abstract

A theorem of Skubenko asserts that if L is a lattice in R5, then there exist positive real numbers λ1,..., λ5 such that L has five linearly independent points on the boundary of the ellipsoid Σ5 i=1 λix2i ≤1 and none other than the origin in its interior. A different proof of this result is given for the case when L has homogeneous minimum different from zero.

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