Well-rounded twists of ideal lattices from real quadratic fields

Mohamed Taoufiq Damir, David Karpuk*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)


We study ideal lattices in R2 coming from real quadratic fields, and give an explicit method for computing all well-rounded twists of any such ideal lattice. We apply this to ideal lattices coming from Markoff numbers to construct infinite families of non-equivalent planar lattices with good sphere-packing radius and good minimum product distance. We also provide a complete classification of all real quadratic fields such that the orthogonal lattice is the only well-rounded twist of the lattice corresponding to the ring of integers.

Original languageEnglish
Pages (from-to)168-196
Number of pages29
JournalJournal of Number Theory
Publication statusPublished - 1 Mar 2019
MoE publication typeA1 Journal article-refereed


  • Ideal lattices
  • Lattices
  • Markoff numbers
  • Real quadratic fields
  • Well-rounded lattices


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