Stability of ideal lattices from quadratic number fields
Number Theory
2015-08-06 v2
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.
Keywords
Cite
@article{arxiv.1402.2738,
title = {Stability of ideal lattices from quadratic number fields},
author = {Lenny Fukshansky},
journal= {arXiv preprint arXiv:1402.2738},
year = {2015}
}
Comments
Theorem 1.2 of the previous version was incorrect as stated, it is now removed