{"paper":{"title":"Normality of the Thue--Morse sequence along Piatetski-Shapiro sequences, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Clemens M\\\"ullner, Lukas Spiegelhofer","submitted_at":"2015-11-05T09:38:19Z","abstract_excerpt":"We prove that the Thue--Morse sequence $\\mathbf t$ along subsequences indexed by $\\lfloor n^c\\rfloor$ is normal, where $1<c<3/2$. That is, for $c$ in this range and for each $\\omega\\in\\{0,1\\}^L$, where $L\\geq 1$, the set of occurrences of $\\omega$ as a subword (contiguous finite subsequence) of the sequence $n\\mapsto \\mathbf t_{\\lfloor n^c\\rfloor}$ has asymptotic density $2^{-L}$. This is an improvement over a recent result by the second author, which handles the case $1<c<4/3$.\n  In particular, this result shows that for $1<c<3/2$ the sequence $n\\mapsto \\mathbf t_{\\lfloor n^c\\rfloor}$ attains"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01671","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"}