{"paper":{"title":"Number theoretic applications of a class of Cantor series fractal functions,I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bill Mance","submitted_at":"2013-10-09T07:22:32Z","abstract_excerpt":"Suppose that $(P,Q) \\in \\mathbb{N}_2^{\\mathbb{N}} \\times \\mathbb{N}_2^{\\mathbb{N}}$ and $x=E_0.E_1E_2\\cdots$ is the $P$-Cantor series expansion of $x \\in \\mathbb{R}$. We define $\\psi_{P,Q}(x):=\\sum_{n=1}^\\infty \\frac {\\min(E_n,q_n-1)} {q_1 \\cdots q_n}$. The functions $\\psi_{P,Q}$ are used to construct many pathological examples of normal numbers. These constructions are used to give the complete containment relation between the sets of $Q$-normal, $Q$-ratio normal, and $Q$-distribution normal numbers and their pairwise intersections for fully divergent $Q$ that are infinite in limit. We analyz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2377","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"}