Diffraction from visible lattice points and k-th power free integers

dc.creatorBaake, Michael
dc.creatorMoody, Robert V.
dc.creatorPleasants, Peter A. B.
dc.date1999-06-19
dc.date2000-01-14
dc.date.accessioned2026-07-07T05:29:35Z
dc.date.available2026-07-07T05:29:35Z
dc.descriptionWe 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.
dc.description45 pages, with minor corrections and improvements; dedicated to Ludwig Danzer on the occasion of his 70th birthday
dc.identifierhttps://arxiv.org/abs/math/9906132
dc.identifierhttp://arxiv.org/abs/math/9906132
dc.identifierDiscr. Math. 221 (2000) 3-42
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78692
dc.subjectMetric Geometry
dc.subjectMathematical Physics
dc.subjectNumber Theory
dc.titleDiffraction from visible lattice points and k-th power free integers
dc.typetext

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