Well-Rounded Twists of Ideal Lattices from Real Quadratic Fields

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 wit...

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Veröffentlicht in:arXiv.org 2018-09
Hauptverfasser: Mohamed Taoufiq Damir, Karpuk, David
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Integers
Lattices
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description 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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title Well-Rounded Twists of Ideal Lattices from Real Quadratic Fields
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