{"paper":{"title":"Piatetski-Shapiro sequences via Beatty sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lukas Spiegelhofer","submitted_at":"2017-07-17T11:11:33Z","abstract_excerpt":"Integer sequences of the form $\\lfloor n^c\\rfloor$, where $1<c<2$, can be locally approximated by sequences of the form $\\lfloor n\\alpha+\\beta\\rfloor$ in a very good way. Following this approach, we are led to an estimate of the difference \\[\\sum_{n\\leq x}\\varphi\\left(\\lfloor n^c\\rfloor\\right)-\\frac 1c\\sum_{n\\leq x^c}\\varphi(n)n^{\\frac 1c-1},\\] which measures the deviation of the mean value of $\\varphi$ on the subsequence $\\lfloor n^c\\rfloor$ from the expected value, by an expression involving exponential sums. As an application we prove that for $1<c\\leq 1.42$ the subsequence of the Thue-Mors"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05094","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"}