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arXiv · 1703.08765

On the Standard Lattices

Rongquan Feng·Longke Tang·Kun Wang
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Abstract

A lattice in the Euclidean space is standard if it has a basis consisting vectors whose norms equal to the length in its successive minima. In this paper, it is shown that with the $L^2$ norm all lattices of dimension $n$ are standard if and only if $n\leqslant 4$. It is also proved that with an arbitrary norm, every lattice of dimensions 1 and 2 is standard. An example of non-standard lattice of dimension $n\geqslant 3$ is given when the lattice is with the $L^1$ norm.

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Rongquan Feng, Longke Tang, Kun Wang. 2017-03-26. On the Standard Lattices. https://arxiv.org/abs/1703.08765

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