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- W3023693569 abstract "Motivated by long-standing conjectures on the discretization of classical inequalities in the Geometry of Numbers, we investigate a new set of parameters, which we call emph{packing minima}, associated to a convex body $K$ and a lattice $Lambda$. These numbers interpolate between the successive minima of $K$ and the inverse of the successive minima of the polar body of $K$, and can be understood as packing counterparts to the covering minima of Kannan & Lov'{a}sz (1988). As our main results, we prove sharp inequalities that relate the volume and the number of lattice points in $K$ to the sequence of packing minima. Moreover, we extend classical transference bounds and discuss a natural class of examples in detail." @default.
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- W3023693569 date "2021-01-16" @default.
- W3023693569 modified "2023-10-03" @default.
- W3023693569 title "Packing minima and lattice points in convex bodies" @default.
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- W3023693569 doi "https://doi.org/10.2140/moscow.2021.10.25" @default.
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