{"paper":{"title":"Chebyshev constants for the unit circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.MG","authors_text":"Gergely Ambrus, Keith M. Ball, T. Erd\\'elyi","submitted_at":"2010-06-26T16:52:09Z","abstract_excerpt":"It is proven that for any system of n points z_1, ..., z_n on the (complex) unit circle, there exists another point z of norm 1, such that\n  $$\\sum 1/|z-z_k|^2 \\leq n^2/4.$$ Equality holds iff the point system is a rotated copy of the nth unit roots.\n  Two proofs are presented: one uses a characterisation of equioscillating rational functions, while the other is based on Bernstein's inequality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5153","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"}