{"paper":{"title":"On the zeros of orthogonal polynomials on the unit circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jes\\'us Mar\\'ia Montaner, Manuel Bello-Hern\\'andez, Mar\\'ia Pilar Alfaro","submitted_at":"2011-08-31T06:02:19Z","abstract_excerpt":"Let ${z_n}$ be a sequence in the unit disk ${z\\in\\mathbb{C}:|z|<1}$. It is known that there exists a unique positive Borel measure in the unit circle ${z\\in\\mathbb{C}:|z|=1}$ such that the orthogonal polynomials ${\\Phi_n}$ satisfy [\\Phi_n(z_n)=0] for each $n=1,2,...$. Characteristics of the orthogonality measure and asymptotic properties of the orthogonal polynomial are given in terms of asymptotic behavior of the sequence ${z_n}$. Particular attention is paid to periodic sequence of zeros ${z_n}$ of period two and three."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.6130","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"}