Well-Rounded Twists of Ideal Lattices from Real Quadratic Fields

2018/06/11 by Damir, Mohamed Taoufiq, Karpuk, David · 3 citations
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1806.04174

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.

Cited by

• Well-Rounded Twists of the Ring of Integers in Cyclic Cubic Fields
• Principal Well-Rounded Ideals of real quadratic fields
• On lattices generated by algebraic conjugates of prime degree

Related

• A complete classification of well-rounded real quadratic ideal lattices
• Canonical basis twists of ideal lattices from real quadratic number fields
• Stability of ideal lattices from quadratic number fields
• Well-Rounded Lattices via Polynomials
• Well-Rounded Twists of the Ring of Integers in Cyclic Cubic Fields