{"paper":{"title":"Metric results on the discrepancy of sequences $\\left(a_{n} \\alpha\\right)_{n \\geq 1}$ modulo one for integer sequences $\\left(a_{n}\\right)_{n \\geq 1}$ of polynomial growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.DS"],"primary_cat":"math.NT","authors_text":"Christoph Aistleitner, Gerhard Larcher","submitted_at":"2015-07-01T12:38:16Z","abstract_excerpt":"An important result of H. Weyl states that for every sequence $\\left(a_{n}\\right)_{n \\geq 1}$ of distinct positive integers the sequence of fractional parts of $\\left(a_{n} \\alpha \\right)_{n\\geq 1}$ is uniformly distributed modulo one for almost all $\\alpha$. However, in general it is a very hard problem to calculate the precise order of convergence of the discrepancy of $\\left(\\left\\{a_{n} \\alpha\\right\\}\\right)_{n \\geq 1}$ for almost all $\\alpha$. In particular it is very difficult to give sharp lower bounds for the speed of convergence. Until now this was only carried out for lacunary sequen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00207","kind":"arxiv","version":4},"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"}