{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:4SSXU2XEIKMJXCYFLQJHLYWP5B","short_pith_number":"pith:4SSXU2XE","schema_version":"1.0","canonical_sha256":"e4a57a6ae442989b8b055c1275e2cfe8571123960d06fe8320d50c02da6d435d","source":{"kind":"arxiv","id":"2308.06839","version":1},"attestation_state":"computed","paper":{"title":"Generalized divisor functions in arithmetic progressions: I","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David T. Nguyen","submitted_at":"2023-08-13T19:46:28Z","abstract_excerpt":"We prove some distribution results for the $k$-fold divisor function in arithmetic progressions to moduli that exceed the square-root of length $X$ of the sum, with appropriate constrains and averaging on the moduli, saving a power of $X$ from the trivial bound. On assuming the Generalized Riemann Hypothesis, we obtain uniform power saving error terms that are independent of $k$.\n  We follow and specialize Y.T. Zhang's method on bounded gaps between primes to our setting. Our arguments are essentially self-contained, with the exception on the use of Deligne's work on the Riemann Hypothesis for"},"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":"2308.06839","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-08-13T19:46:28Z","cross_cats_sorted":[],"title_canon_sha256":"84972a5b46c78da1a7151849678c9d6a2d564baf9f98b275a527d3684a591c35","abstract_canon_sha256":"df8ced213df4686b8c31a10d396617481feea7dafc5dd251a9a7a5721fca20bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:40:45.764287Z","signature_b64":"d3pDp9a9CZvjIm1A14y6FM8vQ16+ZSCrsG7EDbf5gKNZpjSArF2qdkMJNBZaC+0vUI+IFx7P1j0mmzpYc7TFDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4a57a6ae442989b8b055c1275e2cfe8571123960d06fe8320d50c02da6d435d","last_reissued_at":"2026-07-05T06:40:45.763888Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:40:45.763888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized divisor functions in arithmetic progressions: I","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David T. Nguyen","submitted_at":"2023-08-13T19:46:28Z","abstract_excerpt":"We prove some distribution results for the $k$-fold divisor function in arithmetic progressions to moduli that exceed the square-root of length $X$ of the sum, with appropriate constrains and averaging on the moduli, saving a power of $X$ from the trivial bound. On assuming the Generalized Riemann Hypothesis, we obtain uniform power saving error terms that are independent of $k$.\n  We follow and specialize Y.T. Zhang's method on bounded gaps between primes to our setting. Our arguments are essentially self-contained, with the exception on the use of Deligne's work on the Riemann Hypothesis for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.06839","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.06839/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2308.06839","created_at":"2026-07-05T06:40:45.763949+00:00"},{"alias_kind":"arxiv_version","alias_value":"2308.06839v1","created_at":"2026-07-05T06:40:45.763949+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.06839","created_at":"2026-07-05T06:40:45.763949+00:00"},{"alias_kind":"pith_short_12","alias_value":"4SSXU2XEIKMJ","created_at":"2026-07-05T06:40:45.763949+00:00"},{"alias_kind":"pith_short_16","alias_value":"4SSXU2XEIKMJXCYF","created_at":"2026-07-05T06:40:45.763949+00:00"},{"alias_kind":"pith_short_8","alias_value":"4SSXU2XE","created_at":"2026-07-05T06:40:45.763949+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/4SSXU2XEIKMJXCYFLQJHLYWP5B","json":"https://pith.science/pith/4SSXU2XEIKMJXCYFLQJHLYWP5B.json","graph_json":"https://pith.science/api/pith-number/4SSXU2XEIKMJXCYFLQJHLYWP5B/graph.json","events_json":"https://pith.science/api/pith-number/4SSXU2XEIKMJXCYFLQJHLYWP5B/events.json","paper":"https://pith.science/paper/4SSXU2XE"},"agent_actions":{"view_html":"https://pith.science/pith/4SSXU2XEIKMJXCYFLQJHLYWP5B","download_json":"https://pith.science/pith/4SSXU2XEIKMJXCYFLQJHLYWP5B.json","view_paper":"https://pith.science/paper/4SSXU2XE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2308.06839&json=true","fetch_graph":"https://pith.science/api/pith-number/4SSXU2XEIKMJXCYFLQJHLYWP5B/graph.json","fetch_events":"https://pith.science/api/pith-number/4SSXU2XEIKMJXCYFLQJHLYWP5B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4SSXU2XEIKMJXCYFLQJHLYWP5B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4SSXU2XEIKMJXCYFLQJHLYWP5B/action/storage_attestation","attest_author":"https://pith.science/pith/4SSXU2XEIKMJXCYFLQJHLYWP5B/action/author_attestation","sign_citation":"https://pith.science/pith/4SSXU2XEIKMJXCYFLQJHLYWP5B/action/citation_signature","submit_replication":"https://pith.science/pith/4SSXU2XEIKMJXCYFLQJHLYWP5B/action/replication_record"}},"created_at":"2026-07-05T06:40:45.763949+00:00","updated_at":"2026-07-05T06:40:45.763949+00:00"}