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arXiv · 1710.08694

A note on the dispersion of admissible lattices

Mario Ullrich
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Abstract

In this note we show that the volume of axis-parallel boxes in $\mathbb{R}^d$ which do not intersect an admissible lattice $\mathbb{L}\subset\mathbb{R}^d$ is uniformly bounded. In particular, this implies that the dispersion of the dilated lattices $N^{-1/d}\mathbb{L}$ restricted to the unit cube is of the (optimal) order $N^{-1}$ as $N$ goes to infinity. This result was obtained independently by V.N. Temlyakov (arXiv:1709.08158).

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Mario Ullrich. 2017-10-24. A note on the dispersion of admissible lattices. https://doi.org/10.1016/j.dam.2018.08.032

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