{"paper":{"title":"Geodesic continued fractions and LLL","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Frits Beukers","submitted_at":"2013-11-03T10:42:41Z","abstract_excerpt":"We discuss a proposal for a continued fraction-like algorithm to determine simultaneous rational approximations to $d$ real numbers $\\alpha_1,\\ldots,\\alpha_d$. It combines an algorithm of Hermite and Lagarias with ideas from LLL-reduction. We dynamically LLL-reduce a quadratic form with parameter $t$ as $t\\downarrow0$. The new idea in this paper is that checking the LLL-conditions consists of solving linear equations in $t$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0455","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":""},"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"}