Well-Rounded Twists of Ideal Lattices from Real Quadratic Fields
We study ideal lattices in $\mathbb{R}^2$ 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...
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Zusammenfassung: | We study ideal lattices in $\mathbb{R}^2$ 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. |
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DOI: | 10.48550/arxiv.1806.04174 |