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For example, we show that if $X=G/\\Gamma$ is a nilmanifold, $b\\in G$ is an ergodic nilrotation, and $c\\in \\R\\setminus \\Z$ is positive, then the sequence $(b^{[n^c]}x)_{n\\in\\N}$ is equidistributed in $X$ for every $x\\in X$. This is also the case when $n^c$ is replaced with $a(n)$, where $a(t)$ is a function that belongs to some Hardy field, has polynomial growth, and stays logarithmically away from polynomials, and whe"},"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":"0810.4661","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-10-27T02:31:31Z","cross_cats_sorted":[],"title_canon_sha256":"101bfad59b308229ee97ea280cca9b7df20aea52bfe519347c26f97b6af1e5cd","abstract_canon_sha256":"fb47b283e5fb6833b1358b694eefbd6b640fb2089cd715ee8f560b9ea85e369a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:39.860794Z","signature_b64":"PdpSh9tY0Mg+yZv1orVsVuONeEe2/w1Hdcffta5QecCtWp/U9uL0JGY7mtfkRn7lu6POaAGkLNCtKbrGKtTwAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fee60274166dc1d32877d056d4aa7cce0a9bb24bd6fc9c5bfb38417680829c3","last_reissued_at":"2026-05-18T04:01:39.860175Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:39.860175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equidistribution of sparse sequences on nilmanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Nikos Frantzikinakis","submitted_at":"2008-10-27T02:31:31Z","abstract_excerpt":"We study equidistribution properties of nil-orbits $(b^nx)_{n\\in\\N}$ when the parameter $n$ is restricted to the range of some sparse sequence that is not necessarily polynomial. 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