International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 741-748
Visible point vector summations from hypercube and hyperpyramid lattices
Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra ACT 0200, Australia
Received 11 February 1997
Copyright © 1998 Geoffrey B. Campbell. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
New identities are given, based on ideas related to visible (from the origin) point vectors. Each result was found from summing on vpv lattices dividing space
into radial regions from the origin. This is
related to recent work by the author in which new partition type infinite products were derived. Also
recently, Baake et al  and Mosseri  considered the 2-
visible lattice points as part of an optical
experiment in which the so-called Optical Fourier Transform was applied. Many of the techniques
espoused in Glasser and Zucker , and in Ninham et al  involving Mellin and Möbius inversions
are applicable also to the current paper.