On Lattice points and Optimal Packing of Minkowski's Balls and Domains
Number Theory
2023-05-26 v1
Abstract
We investigate lattice packings of Minkowski's balls and domains, as well as the distribution of lattice points on Minkowski's curves which are boundaries of Minkowski's balls. By results of the proof of Minkowski's conjecture about the critical determinant we devide the balls and domains on 3 classes: Minkowski, Davis and Chebyshev-Cohn balls. The optimal lattice packings of the balls and domains are obtained. The minimum areas of hexagons inscribed in the balls and domains and circumscribed around their are given. We construct direct systems of these balls, domains and their critical lattices and calculate their direct limits.
Keywords
Cite
@article{arxiv.2305.15739,
title = {On Lattice points and Optimal Packing of Minkowski's Balls and Domains},
author = {Nikolaj Glazunov},
journal= {arXiv preprint arXiv:2305.15739},
year = {2023}
}
Comments
16 pages. arXiv admin note: text overlap with arXiv:2302.01644, arXiv:2211.16873