{"paper":{"title":"A critical majorant for the Khinchin-Ostrowski property","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CV","authors_text":"Bartosz Malman","submitted_at":"2025-06-07T20:18:41Z","abstract_excerpt":"In this short note we prove an optimal version of a classical result. Given a majorant determining a growth restriction on functions in the unit disk $\\mathbb{D}$, we say that a set $E$ on the unit circle $\\mathbb{T}$ is a uniqueness set, or has the Khinchin-Ostrowski property, with respect to the majorant, if any sequence of analytic polynomials satisfying the growth restriction which converges in an appropriate sense to $0$ on $E$, in fact is forced to converge to $0$ in $\\mathbb{D}$ also. Theorems proved by Kegejan and Khrushchev state that if $E$ has positive Lebesgue measure and satisfies"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.06911","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.06911/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}