Diffraction from visible lattice points and k-th power free integers
| dc.creator | Baake, Michael | |
| dc.creator | Moody, Robert V. | |
| dc.creator | Pleasants, Peter A. B. | |
| dc.date | 1999-06-19 | |
| dc.date | 2000-01-14 | |
| dc.date.accessioned | 2026-07-07T05:29:35Z | |
| dc.date.available | 2026-07-07T05:29:35Z | |
| dc.description | 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. | |
| dc.description | 45 pages, with minor corrections and improvements; dedicated to Ludwig Danzer on the occasion of his 70th birthday | |
| dc.identifier | https://arxiv.org/abs/math/9906132 | |
| dc.identifier | http://arxiv.org/abs/math/9906132 | |
| dc.identifier | Discr. Math. 221 (2000) 3-42 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78692 | |
| dc.subject | Metric Geometry | |
| dc.subject | Mathematical Physics | |
| dc.subject | Number Theory | |
| dc.title | Diffraction from visible lattice points and k-th power free integers | |
| dc.type | text |