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Bases of minimal vectors in tame lattices

Volume 205 / 2022

Mohamed Taoufiq Damir, Guillermo Mantilla-Soler Acta Arithmetica 205 (2022), 265-285 MSC: Primary 11H06; Secondary 11H50, 11R21. DOI: 10.4064/aa220408-18-8 Published online: 8 September 2022


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.


  • Mohamed Taoufiq DamirDepartment of Computer Science
    University of Helsinki
    FI-00014 Helsinki, Finland
  • Guillermo Mantilla-SolerDepartment of Mathematics
    Universidad Nacional de Colombia
    Sede Medellín
    050034 Medellín, Colombia

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