English

Some remarks on the visible points of a lattice

Mathematical Physics 2014-09-30 v1 math.MP

Abstract

We comment on the set of visible points of a lattice and its Fourier transform, thus continuing and generalizing previous work by Schroeder and Mosseri. A closed formula in terms of Dirichlet series is obtained for the Bragg part of the Fourier transform. We compare this calculation with the outcome of an optical Fourier transform of the visible points of the 2D square lattice.

Keywords

Cite

@article{arxiv.math-ph/9903046,
  title  = {Some remarks on the visible points of a lattice},
  author = {Michael Baake and Uwe Grimm and David Warrington},
  journal= {arXiv preprint arXiv:math-ph/9903046},
  year   = {2014}
}

Comments

9 pages, 3 eps-figures, 1 jpeg-figure; updated version; another article (by M. Baake, R. V. Moody and P. A. B. Pleasants) with the complete solution of the spectral problem will follow soon (see math.MG/9906132)