{"paper":{"title":"On sequences with prescribed metric discrepancy behavior","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christoph Aistleitner, Gerhard Larcher","submitted_at":"2015-07-23T12:48:14Z","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 $\\left(a_{n} \\alpha \\right)_{n \\geq1}$ 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 $D_{N}$ of $\\left(\\left\\{a_{n} \\alpha \\right\\}\\right)_{n \\geq 1}$ for almost all $\\alpha$. By a result of R. C. Baker this discrepancy always satisfies $N D_{N} = \\mathcal{O} \\left(N^{\\frac{1}{2}+\\varepsilon}\\right)$ for almost al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06472","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"}