{"paper":{"title":"Periodicity of Multidimensional Continued Fractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eun Hye Lee","submitted_at":"2018-10-27T16:54:34Z","abstract_excerpt":"It is known that the continued fraction expansion of a real number is periodic if and only if the number is a quadratic irrational. In an attempt to generalize this phenomenon to other settings, Jun-Ichi Tamura and Shin-Ichi Yasutomi have developed a new algorithm for multidimensional continued fractions (Algebraic Jacobi-Perron algorithm) that involves cubic irrationals, and proved periodicity in some cubic number fields, such as $\\mathbb{Q}(\\sqrt[3]{m^3+1})$ where $m\\in\\mathbb{Z}$, and $\\mathbb{Q}(\\delta_m)$ where $\\delta_m$ is a root of $x^3-mx+1=0,\\,\\,m\\in\\mathbb{Z},\\,\\, m\\geq3$ with the a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11676","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"}