{"paper":{"title":"Shortest nonzero lattice points in a totally real multi-quadratic number field and applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jishu Das","submitted_at":"2024-11-04T20:16:00Z","abstract_excerpt":"Let $F$ be a multi-quadratic totally real number field. Let $\\sigma_1,\\dots, \\sigma_r$ denote its distinct embeddings. Given $s \\in F,$ we give an explicit formula for $\\| \\sigma(s)\\|$ and $\\sum_{i<j} \\sigma_i(s)\\sigma_j(s),$ where $\\| \\sigma(s)\\|=\\sqrt{\\sum_{i=1}^r(\\sigma_i(s))^2}.$ Let $\\mathfrak{M}$ be a fractional ideal in $F$ and $\\min\\left( \\mathfrak{M}\\right):=\\min\\{\\|\\sigma(s)\\| \\, | \\, s \\in \\mathfrak{M}, s\\neq 0 \\}.$ The set of shortest nonzero lattice points for $\\mathfrak{M}$ is given by $\\{s\\in \\mathfrak{M} : \\| \\sigma(s)\\|=\\min(\\mathfrak{M}) \\}.$ We provide shortest nonzero latti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.02575","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.02575/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}