{"paper":{"title":"A one-sided power sum inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Frits Beukers, Rob Tijdeman","submitted_at":"2011-07-27T14:48:45Z","abstract_excerpt":"In this note we prove results of the following types. Let be given distinct complex numbers $z_j$ satisfying the conditions $|z_j| = 1, z_j \\not= 1$ for $j=1,..., n$ and for every $z_j$ there exists an $ i$ such that $z_i = \\bar{z_j}. $ Then $$\\inf_{k} \\sum_{j=1}^n z_j^k \\leq - 1. $$ If, moreover, none of the numbers $z_j$ is a root of unity, then $$\\inf_{k} \\sum_{j=1}^n z_j^k \\leq - \\frac {2} {\\pi^3} \\log n. $$ The constant -1 in the former result is the best possible. The above results are special cases of upper bounds for $\\inf_{k} \\sum_{j=1}^n b_jz_j^k$ obtained in this paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5495","kind":"arxiv","version":3},"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"}