{"paper":{"title":"Lower bounds on the projective heights of algebraic points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Charles L. Samuels","submitted_at":"2014-08-21T15:59:55Z","abstract_excerpt":"If $\\alpha_1,\\ldots,\\alpha_r$ are algebraic numbers such that $$N=\\sum_{i=1}^r\\alpha_i \\ne \\sum_{i=1}^r\\alpha_i^{-1}$$ for some integer $N$, then a theorem of Beukers and Zagier gives the best possible lower bound on $$\\sum_{i=1}^r\\log h(\\alpha_i)$$ where $h$ denotes the Weil Height. We will extend this result to allow $N$ to be any totally real algebraic number. Our generalization includes a consequence of a theorem of Schinzel which bounds the height of a totally real algebraic integer."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5048","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"}