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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.05094","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-17T11:11:33Z","cross_cats_sorted":[],"title_canon_sha256":"b6d73f2880d784f62e5811477529eec03c13228ea517842701ae3563633242d3","abstract_canon_sha256":"224587c1407f6615d8e33073273d36bc711576173f15221ced9a95548ee53b0f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:11.407192Z","signature_b64":"cW97BppzMaLJYkgoHdDxhw6mJ5jqnZE0svVu9T02M1mGO4w7pKB6e2rtGICO6Kj6X/7qopMvA4CQCpk1C1EVDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0fcd37ab68fb76bdd75414f1fc3b6092eac74e0c770da3ee231f1f46d1b7f739","last_reissued_at":"2026-05-18T00:40:11.406711Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:11.406711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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