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We show that $(f(n))_{n \\in \\mathbb{N}}$ is uniformly distributed mod 1 if and only if $(f(p))_{p \\in \\mathcal{P}}$ is uniformly distributed mod 1. This result is then utilized to derive various ergodic and combinatorial statements which significantly generalize the results obtained in [BKMST]."},"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":"1503.04960","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-17T09:17:59Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"16c67ed99bc74b09c1222aa75f0bc406be52ca02c3adeed32d7d3ee4bb239318","abstract_canon_sha256":"af4e6088d638b4bdff7bbd3368b7c396f1b883788c6b5ce968e3f03b926c0afa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:33.041079Z","signature_b64":"ylTvDala1nv3ZIHF5m+7qyy4Q7U8LrpOrKrD796nP0do6eFGjasspjTCwCAIyEZmue9CwmcezTpv71oXsbPQAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9b28b5149b7f3bb0bf9bc7a9546e51fd6454e3cda3a1f9f1b6cff3e56301c12","last_reissued_at":"2026-05-18T02:17:33.040506Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:33.040506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniform distribution of subpolynomial functions along primes and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Grigori Kolesnik, Vitaly Bergelson, Younghwan Son","submitted_at":"2015-03-17T09:17:59Z","abstract_excerpt":"Let $H$ be a Hardy field (a field consisting of germs of real-valued functions at infinity that is closed under differentiation) and let $f \\in H$ be a subpolynomial function. 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This result is then utilized to derive various ergodic and combinatorial statements which significantly generalize the results obtained in [BKMST]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04960","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1503.04960","created_at":"2026-05-18T02:17:33.040600+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.04960v2","created_at":"2026-05-18T02:17:33.040600+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04960","created_at":"2026-05-18T02:17:33.040600+00:00"},{"alias_kind":"pith_short_12","alias_value":"7GZIWUKJW7Z3","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"7GZIWUKJW7Z3WC7Z","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"7GZIWUKJ","created_at":"2026-05-18T12:29:10.953037+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7GZIWUKJW7Z3WC7ZXR5JKRXFD7","json":"https://pith.science/pith/7GZIWUKJW7Z3WC7ZXR5JKRXFD7.json","graph_json":"https://pith.science/api/pith-number/7GZIWUKJW7Z3WC7ZXR5JKRXFD7/graph.json","events_json":"https://pith.science/api/pith-number/7GZIWUKJW7Z3WC7ZXR5JKRXFD7/events.json","paper":"https://pith.science/paper/7GZIWUKJ"},"agent_actions":{"view_html":"https://pith.science/pith/7GZIWUKJW7Z3WC7ZXR5JKRXFD7","download_json":"https://pith.science/pith/7GZIWUKJW7Z3WC7ZXR5JKRXFD7.json","view_paper":"https://pith.science/paper/7GZIWUKJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.04960&json=true","fetch_graph":"https://pith.science/api/pith-number/7GZIWUKJW7Z3WC7ZXR5JKRXFD7/graph.json","fetch_events":"https://pith.science/api/pith-number/7GZIWUKJW7Z3WC7ZXR5JKRXFD7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7GZIWUKJW7Z3WC7ZXR5JKRXFD7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7GZIWUKJW7Z3WC7ZXR5JKRXFD7/action/storage_attestation","attest_author":"https://pith.science/pith/7GZIWUKJW7Z3WC7ZXR5JKRXFD7/action/author_attestation","sign_citation":"https://pith.science/pith/7GZIWUKJW7Z3WC7ZXR5JKRXFD7/action/citation_signature","submit_replication":"https://pith.science/pith/7GZIWUKJW7Z3WC7ZXR5JKRXFD7/action/replication_record"}},"created_at":"2026-05-18T02:17:33.040600+00:00","updated_at":"2026-05-18T02:17:33.040600+00:00"}