Abstract
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 language | English |
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Pages (from-to) | 168-196 |
Number of pages | 29 |
Journal | Journal of Number Theory |
Volume | 196 |
DOIs | |
Publication status | Published - 1 Mar 2019 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Ideal lattices
- Lattices
- Markoff numbers
- Real quadratic fields
- Well-rounded lattices