Publication:
Interpolating between volume and lattice point enumerator with successive minima

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Date
2022-05-11
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Authors
Freyer, Ansgar ; Lucas Marín, Eduardo
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Facultad de Matemáticas
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Publisher
Springer
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Matemáticas
DOI
https://doi.org/10.1007/s00605-022-01713-1
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info:eu-repo/semantics/article
Description
Abstract
We study inequalities that simultaneously relate the number of lattice points, the volume and the successive minima of a convex body to one another. One main ingredient in order to establish these relations is Blaschke’s shaking procedure, by which the problem can be reduced from arbitrary convex bodies to anti-blocking bodies. As a consequence of our results, we obtain an upper bound on the lattice point enumerator in terms of the successive minima, which is equivalent to Minkowski’s upper bound on the volume in terms of the successive minima.
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Successive minima , Minkowski’s second theorem , Blaschke’s shaking procedure , Lattice points in convex bodies
Citation
Monatsh Math 198, 717–740 (2022)
URI
http://hdl.handle.net/10201/214361
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