Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diffraction from visible lattice points and k-th power free integers   We prove that the set of visible points of any lattice of dimension at least
2 has pure point diffraction spectrum, and we determine the diffraction
spectrum explicitly. This settles previous speculation on the exact nature of
the diffraction in this situation, see math-ph/9903046 and references therein.
Using similar methods we show the same result for the 1-dimensional set of k-th
power free integers with k at least 2. Of special interest is the fact that
neither of these sets is a Delone set --- each has holes of unbounded inradius.
We provide a careful formulation of the mathematical ideas underlying the study
of diffraction from infinite point sets.

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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con