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Stability of ideal lattices from quadratic number fields

We study semi-stable ideal lattices coming from real quadratic number fields. Specifically, we demonstrate infinite families of semi-stable and unstable ideal lattices of trace type, establishing explicit conditions on the canonical basis of an ideal that ensure stability; in particular, our result implies that an ideal lattice of trace type coming from a real quadratic field is semi-stable with positive probability. We also briefly discuss the connection between stability and well-roundedness of Euclidean lattices.

preprint2015arXivOpen access
Lenny Fukshansky
math.NT
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Lenny Fukshansky

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