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arXiv · 2006.16794

Bases of minimal vectors in tame lattices

Mohamed Taoufiq Damir·Guillermo Mantilla-Soler
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Abstract

Motivated by the behavior of the trace pairing over tame cyclic number fields, we introduce the notion of tame lattices. Given an arbitrary non-trivial lattice $\mathcal{L}$ we construct a parametric family of full-rank sub-lattices $\{\mathcal{L}_{\alpha}\}$ of $\mathcal{L}$ such that whenever $\mathcal{L}$ is tame each $\mathcal{L}_{\alpha}$ has a basis of minimal vectors. Furthermore, for each $\mathcal{L}_{\alpha}$ in the family a basis of minimal vectors is explicitly constructed.

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Mohamed Taoufiq Damir, Guillermo Mantilla-Soler. 2020-06-30. Bases of minimal vectors in tame lattices. https://arxiv.org/abs/2006.16794

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