{"paper":{"title":"Quantitative version of Beurling-Helson theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"math.CA","authors_text":"Ilya D. Shkredov, Sergei V. Konyagin","submitted_at":"2014-01-17T18:30:47Z","abstract_excerpt":"It is proved that any continuous function f on the unit circle such that the sequence e^{in f}, n=1,2,... has small Wiener norm \\| e^{in f} \\|_A = o (\\frac{\\log^{1/22} |n|}{(\\log \\log |n|)^{3/11}}), is linear. Moreover, we get lower bounds for Wiener norm of characteristic functions of subsets from Z_p in the case of prime p."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4429","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"}