A reverse Minkowski theorem.
STOC(2017)
摘要
We prove a conjecture due to Dadush, showing that if Lâ ân is a lattice such that det(Lâ²) ⥠1 for all sublattices Lâ² â L, then
where t := 10(logn + 2). This implies bounds on the number of lattice points in Euclidean balls for various different radii, which can be seen as a reverse form of Minkowskiâs First Theorem.更多
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关键词
Lattices,Geometry of numbers
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