{"paper":{"title":"Minkowski's theorem on independent conjugate units","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jeffrey D. Vaaler, Shabnam Akhtari","submitted_at":"2016-08-13T03:45:51Z","abstract_excerpt":"We call a unit $\\beta$ in a Galois extension $l/\\mathbb{Q}$ a Minkowski unit if the subgroup generated by $\\beta$ and its conjugates over $\\mathbb{Q}$ has maximum rank in the unit group of $l$. Minkowski showed the existence of such units in every Galois extension. We will give a new proof to Minkowski's theorem and show that there exists a Minkowski unit $\\beta \\in l$ such that the Weil height of $\\beta$ is comparable with the sum of the heights of a fundamental system of units of $l$. Our proof implies a bound on the index of the subgroup generated by the algebraic conjugates of $\\beta$ in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03935","kind":"arxiv","version":2},"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"}