Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equality case in van der Corput's inequality and collisions in multiple
  lattice tilings   Van der Corput's provides the sharp bound vol(C) \le m 2^d on the volume of a
d-dimensional origin-symmetric convex body C that has 2m-1 points of the
integer lattice in its interior. For m=1, a characterization of the equality
case vol(C)= m 2^d is equivalent to the well-known problem of characterizing
tilings by translations of a convex body. It is rather surprising that so far,
for m \ge 2, no characterization of the equality case has been available,
though a hint to the respective characterization problem can be found in the
1987 monograph of Gruber and Lekkerkerker. We give an explicit characterization
of the equality case for all m \ge 2. Our result reveals that, the equality
case for m \ge 2 is more restrictive than for $m=1$. We also present
consequences of our characterization in the context of multiple lattice
tilings.

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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: adap-org