Article - postprint
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.
© 2015 Fukshansky
Fukshansky, Lenny. "Stability of ideal lattices from quadratic number fields." The Ramanujan Journal, vol. 37 no. 2 (2015), pg. 243--256.