{"paper":{"title":"Recurrence and non-uniformity of bracket polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.DS"],"primary_cat":"math.NT","authors_text":"Matthew Tointon","submitted_at":"2013-09-25T11:41:44Z","abstract_excerpt":"A bracket polynomial on the integers is a function formed using the operations of addition, multiplication and taking fractional parts. For a fairly large class of bracket polynomials we show that if p is a bracket polynomial of degree k-1 on [N] then the function f defined by f(n) = e(p(n)) has Gowers U^k[N]-norm bounded away from zero, uniformly in N.\n  We establish this result by first reducing it to a certain recurrence property of sets of bracket polynomials. Specifically, for a fairly large class of bracket polynomials we show that if p_1, ..., p_r are bracket polynomials then their valu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6470","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"}