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- W1964610978 abstract "Let ℝ n be the n-dimensional Euclidean space with O as the origin. Let ∧ be a lattice of determinant 1 such that there is a sphere |X| < R which contains no point of ∧ other than O and has n linearly independent points of ∧ on its boundary. A well known conjecture in the geometry of numbers asserts that any closed sphere in ℝ n of radius $ sqrt {n/4}$ contains a point of ∧. This is known to be true for n≤8. Here we prove a more general conjecture of Woods for n = 9 from which this conjecture follows in ℝ9. Together with a result of McMullen (J. Amer. Math. Soc. 18 (2005) 711–734), the long standing conjecture of Minkowski follows for n = 9." @default.
- W1964610978 created "2016-06-24" @default.
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- W1964610978 date "2016-08-10" @default.
- W1964610978 modified "2023-09-24" @default.
- W1964610978 title "On conjectures of Minkowski and Woods for n = 9" @default.
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- W1964610978 doi "https://doi.org/10.1007/s12044-016-0295-2" @default.
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