Stability of Ideal Lattices from Quadratic Number Fields

Authors

Lenny Fukshansky, Claremont McKenna CollegeFollow

Document Type

Article - postprint

Department

Mathematics (CMC)

Publication Date

2015

Abstract

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.

Comments

Source: Author's post-print manuscript in PDF.

Rights Information

© 2015 Fukshansky

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Recommended Citation

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