English

Bases of minimal vectors in tame lattices

Number Theory 2022-04-14 v3

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 L\mathcal{L} we construct a parametric family of full-rank sub-lattices {Lα}\{\mathcal{L}_{\alpha}\} of L\mathcal{L} such that whenever L\mathcal{L} is tame each Lα\mathcal{L}_{\alpha} has a basis of minimal vectors. Furthermore, for each Lα\mathcal{L}_{\alpha} in the family a basis of minimal vectors is explicitly constructed.

Keywords

Cite

@article{arxiv.2006.16794,
  title  = {Bases of minimal vectors in tame lattices},
  author = {Mohamed Taoufiq Damir and Guillermo Mantilla-Soler},
  journal= {arXiv preprint arXiv:2006.16794},
  year   = {2022}
}