{"paper":{"title":"Point evaluation for polynomials on the circle","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Sarah May Instanes","submitted_at":"2025-09-26T08:12:55Z","abstract_excerpt":"We study the constant $\\mathscr{C}_{d,p}$ defined as the smallest constant $C$ such that $\\|P\\|_\\infty^p \\leq C\\|P\\|_p^p$ holds for every polynomial $P$ of degree $d$, where we consider the $L^p$ norm on the unit circle. We conjecture that $\\mathscr{C}_{d,p} \\leq dp/2+1$ for all $p \\geq 2$ and all degrees $d$. We show that the conjecture holds for all $p \\geq 2$ when $d \\leq 4$ and for all $d$ when $p \\geq 6.8$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.22035","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"}