{"paper":{"title":"Technical Details of the Proof of the Sine Inequality \\\\[1.2ex] {\\normalsize $\\displaystyle \\sum_{k=1}^{n-1}\\left( \\frac{n}{k} - \\frac{k}{n} \\right) ^\\beta \\sin(kx) \\geq 0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Man Kam Kwong","submitted_at":"2017-02-11T06:22:42Z","abstract_excerpt":"In a recent study, H. Alzer and the author showed that the sine polynomial $$ \\sum_{k=1}^{n-1} \\left( \\frac{n}{k} - \\frac{k}{n} \\right) ^\\beta \\,\\sin(kx) > 0 $$ is nonnegative for $ x\\in[0,\\pi ] $, $ n\\geq 2, \\, \\beta \\geq \\beta _1 := \\frac{\\log(2)}{\\log(16/5)} . $ This result, among others, will be presented in a forthcoming article. The proof relies on quite a number of technical Lemmas and inequalities. We have decided to delegate all the tedious details of the proofs of these Lemmas in a separate article, namely, the current one. Some of the proofs require brute-force numerical computation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03387","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"}