{"paper":{"title":"Estimates for the norms of products of sines and cosines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CA","authors_text":"Jordan Bell","submitted_at":"2012-10-27T22:47:53Z","abstract_excerpt":"In this paper we prove asymptotic formulas for the $L^p$ norms of $P_n(\\theta)=\\prod_{k=1}^n (1-e^{ik\\theta})$ and $Q_n(\\theta)=\\prod_{k=1}^n (1+e^{ik\\theta})$. These products can be expressed using $\\prod_{k=1}^n \\sin\\Big(\\frac{k\\theta}{2}\\Big)$ and $\\prod_{k=1}^n \\cos\\Big(\\frac{k\\theta}{2}\\Big)$ respectively. We prove an estimate for $P_n$ at a point near where its maximum occurs. Finally, we give an asymptotic formula for the maximum of the Fourier coefficients of $Q_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7380","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"}