International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 4, Pages 271-277
Infinite products over hyperpyramid lattices
Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, ACT, Canberra 0200, Australia
Received 2 July 1998
Copyright © 2000 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 infinite product identities are given, based on summed
visible (from the origin) point vectors. Each result
is found from summing on vpv lattices dividing space into radial
regions from the origin. Recently, Baake et al. and Mosseri
considered the 2-D visible lattice points as part of an optical
experiment in which so-called Optical Fourier Transform was
applied. Many of the techniques exposed by Glasser and Zucker, and
Ninham et al. involving Mellin and Möbius inversions are also
applicable to the current paper.