{"paper":{"title":"An inequality for the norm of a polynomial factor","license":"","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CV","authors_text":"Igor E. Pritsker","submitted_at":"2000-01-24T19:20:07Z","abstract_excerpt":"Let $p(z)$ be a monic polynomial of degree $n$, with complex coefficients, and let $q(z)$ be its monic factor. We prove an asymptotically sharp inequality of the form $\\|q\\|_{E} \\le C^n \\|p\\|_E$, where $\\|\\cdot\\|_E$ denotes the sup norm on a compact set $E$ in the plane. The best constant $C_E$ in this inequality is found by potential theoretic methods. We also consider applications of the general result to the cases of a disk and a segment."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0001124","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"}