{
  "id": "1402.2738",
  "version": "v2",
  "published": "2014-02-12T05:25:07.000Z",
  "updated": "2015-08-05T17:04:17.000Z",
  "title": "Stability of ideal lattices from quadratic number fields",
  "authors": [
    "Lenny Fukshansky"
  ],
  "comment": "Theorem 1.2 of the previous version was incorrect as stated, it is now removed",
  "categories": [
    "math.NT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-12T05:25:07.000Z",
      "abstract": "We study semi-stable ideal lattices coming from quadratic number fields. We prove that all ideal lattices of trace type from rings of integers of imaginary quadratic number fields are semi-stable. For real quadratic fields, we demonstrate infinite families of semi-stable and unstable ideal lattices, 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.",
      "comment": "12 pages, to appear in the Ramanujan Journal",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-08-05T17:04:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11H06",
      "11R11",
      "11E16",
      "11H55"
    ],
    "keywords": [
      "real quadratic field",
      "trace type",
      "imaginary quadratic number fields",
      "demonstrate infinite families",
      "study semi-stable ideal lattices coming"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.2738F"
    }
  }
}