{"paper":{"title":"Cantor series constructions of sets of normal numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bill Mance","submitted_at":"2010-10-13T21:52:31Z","abstract_excerpt":"Let $Q=(q_n)_{n=1}^{\\infty}$ be a sequence of integers greater than or equal to 2. We say that a real number $x$ in $[0,1)$ is {\\it $Q$-distribution normal} if the sequence $(q_1q_2... q_n x)_{n=1}^{\\infty}$ is uniformly distributed mod 1. In \\cite{Lafer}, P. Lafer asked for a construction of a $Q$-distribution normal number for an arbitrary $Q$. Under a mild condition on $Q$, we construct a set $\\Theta_Q$ of $Q$-distribution normal numbers. This set is perfect and nowhere dense. Additionally, given any $\\alpha$ in $[0,1]$, we provide an explicit example of a sequence $Q$ such that the Hausdor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2782","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"}