Bases of minimal vectors in tame lattices
Volume 205 / 2022
Acta Arithmetica 205 (2022), 265-285
MSC: Primary 11H06; Secondary 11H50, 11R21.
DOI: 10.4064/aa220408-18-8
Published online: 8 September 2022
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 $\{\mathcal L_{\alpha }\}$ of full-rank sublattices 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.
