{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:PFXHQLJBT5KXOU7LKO2OIU2DYV","short_pith_number":"pith:PFXHQLJB","schema_version":"1.0","canonical_sha256":"796e782d219f557753eb53b4e45343c578f3d65b4000c295955b843032c8c479","source":{"kind":"arxiv","id":"1806.01404","version":1},"attestation_state":"computed","paper":{"title":"Note on the number of divisors of reducible quadratic polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Adrian W. Dudek, {\\L}ukasz Pa\\'nkowski, Victor Scharaschkin","submitted_at":"2018-06-04T21:44:52Z","abstract_excerpt":"In a recent paper, Lapkova uses a Tauberian theorem to derive the asymptotic formula for the divisor sum $\\sum_{n \\leq x} d( n (n+v))$ where $v$ is a fixed integer and $d(n)$ denotes the number of divisors of $n$. We reprove her result by following a suggestion of Hooley, namely investigating the relationship between this sum and the well-known sum $\\sum_{n \\leq x} d( n ) d (n+v)$. As such, we are able to furnish additional terms in the asymptotic formula."},"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":"1806.01404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-04T21:44:52Z","cross_cats_sorted":[],"title_canon_sha256":"9bb8f37c0ed3414619c044a0d9628d7dfe6d132d8d9903635ab8cef4670b7ee1","abstract_canon_sha256":"619c00bdd46aa359f439ba846123947583f8632cfc9289f26f61145a8a03e8a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:12.479924Z","signature_b64":"BvU8twsAEDLSwekahNMLtYz/IzAmMqzZQnp2+VDcvqeNkNSniXlrL0jb2jg2ctI48dqOisudC6LFUT7Pdf1BDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"796e782d219f557753eb53b4e45343c578f3d65b4000c295955b843032c8c479","last_reissued_at":"2026-05-17T23:53:12.479203Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:12.479203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Note on the number of divisors of reducible quadratic polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Adrian W. Dudek, {\\L}ukasz Pa\\'nkowski, Victor Scharaschkin","submitted_at":"2018-06-04T21:44:52Z","abstract_excerpt":"In a recent paper, Lapkova uses a Tauberian theorem to derive the asymptotic formula for the divisor sum $\\sum_{n \\leq x} d( n (n+v))$ where $v$ is a fixed integer and $d(n)$ denotes the number of divisors of $n$. We reprove her result by following a suggestion of Hooley, namely investigating the relationship between this sum and the well-known sum $\\sum_{n \\leq x} d( n ) d (n+v)$. As such, we are able to furnish additional terms in the asymptotic formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01404","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1806.01404","created_at":"2026-05-17T23:53:12.479328+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.01404v1","created_at":"2026-05-17T23:53:12.479328+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.01404","created_at":"2026-05-17T23:53:12.479328+00:00"},{"alias_kind":"pith_short_12","alias_value":"PFXHQLJBT5KX","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"PFXHQLJBT5KXOU7L","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"PFXHQLJB","created_at":"2026-05-18T12:32:43.782077+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/PFXHQLJBT5KXOU7LKO2OIU2DYV","json":"https://pith.science/pith/PFXHQLJBT5KXOU7LKO2OIU2DYV.json","graph_json":"https://pith.science/api/pith-number/PFXHQLJBT5KXOU7LKO2OIU2DYV/graph.json","events_json":"https://pith.science/api/pith-number/PFXHQLJBT5KXOU7LKO2OIU2DYV/events.json","paper":"https://pith.science/paper/PFXHQLJB"},"agent_actions":{"view_html":"https://pith.science/pith/PFXHQLJBT5KXOU7LKO2OIU2DYV","download_json":"https://pith.science/pith/PFXHQLJBT5KXOU7LKO2OIU2DYV.json","view_paper":"https://pith.science/paper/PFXHQLJB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.01404&json=true","fetch_graph":"https://pith.science/api/pith-number/PFXHQLJBT5KXOU7LKO2OIU2DYV/graph.json","fetch_events":"https://pith.science/api/pith-number/PFXHQLJBT5KXOU7LKO2OIU2DYV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PFXHQLJBT5KXOU7LKO2OIU2DYV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PFXHQLJBT5KXOU7LKO2OIU2DYV/action/storage_attestation","attest_author":"https://pith.science/pith/PFXHQLJBT5KXOU7LKO2OIU2DYV/action/author_attestation","sign_citation":"https://pith.science/pith/PFXHQLJBT5KXOU7LKO2OIU2DYV/action/citation_signature","submit_replication":"https://pith.science/pith/PFXHQLJBT5KXOU7LKO2OIU2DYV/action/replication_record"}},"created_at":"2026-05-17T23:53:12.479328+00:00","updated_at":"2026-05-17T23:53:12.479328+00:00"}