{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:ZDMRJUS2US3JQJB5FVPYNAXDY2","short_pith_number":"pith:ZDMRJUS2","schema_version":"1.0","canonical_sha256":"c8d914d25aa4b698243d2d5f8682e3c6a53dcb38ea516d62f002d656bad75c84","source":{"kind":"arxiv","id":"1205.1706","version":3},"attestation_state":"computed","paper":{"title":"Generations of correlation averages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Giovanni Coppola, Maurizio Laporta","submitted_at":"2012-05-06T08:53:57Z","abstract_excerpt":"The present paper is a dissertation on the possible consequences of a conjectural bound for the so-called \\thinspace modified Selberg integral of the divisor function $d_3$, i.e. a discrete version of the classical Selberg integral, where $d_3(n)=\\sum_{abc=n}1$ is attached to the Cesaro weight $1-|n-x|/H$ in the short interval $|n-x|\\le H$. Mainly, an immediate consequence is a non-trivial bound for the Selberg integral of $d_3$, improving recent results of Ivi\\'c based on the standard approach through the moments of the Riemann zeta function on the critical line. We proceed instead with eleme"},"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":"1205.1706","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-06T08:53:57Z","cross_cats_sorted":[],"title_canon_sha256":"2181b6d48c8b60f89144d42c287fe480f2fe33b48dc725dbbe9a505b6a9d7c3b","abstract_canon_sha256":"57a25ef24d70ef4e8b7b5103ad94ea402f3291342be9579a26f2a675dff10094"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:31.885612Z","signature_b64":"Nz7zL/reV7Uo+xKPxm+o+7JecePOwcJ5FPKgQ/gHkFRB99uWbJZt5iQiVG2SIT7U4zuqeG2XhptHv7adPvY1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8d914d25aa4b698243d2d5f8682e3c6a53dcb38ea516d62f002d656bad75c84","last_reissued_at":"2026-05-18T02:49:31.884980Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:31.884980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generations of correlation averages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Giovanni Coppola, Maurizio Laporta","submitted_at":"2012-05-06T08:53:57Z","abstract_excerpt":"The present paper is a dissertation on the possible consequences of a conjectural bound for the so-called \\thinspace modified Selberg integral of the divisor function $d_3$, i.e. a discrete version of the classical Selberg integral, where $d_3(n)=\\sum_{abc=n}1$ is attached to the Cesaro weight $1-|n-x|/H$ in the short interval $|n-x|\\le H$. Mainly, an immediate consequence is a non-trivial bound for the Selberg integral of $d_3$, improving recent results of Ivi\\'c based on the standard approach through the moments of the Riemann zeta function on the critical line. We proceed instead with eleme"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1706","kind":"arxiv","version":3},"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":"1205.1706","created_at":"2026-05-18T02:49:31.885074+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.1706v3","created_at":"2026-05-18T02:49:31.885074+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1706","created_at":"2026-05-18T02:49:31.885074+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZDMRJUS2US3J","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZDMRJUS2US3JQJB5","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZDMRJUS2","created_at":"2026-05-18T12:27:30.460161+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/ZDMRJUS2US3JQJB5FVPYNAXDY2","json":"https://pith.science/pith/ZDMRJUS2US3JQJB5FVPYNAXDY2.json","graph_json":"https://pith.science/api/pith-number/ZDMRJUS2US3JQJB5FVPYNAXDY2/graph.json","events_json":"https://pith.science/api/pith-number/ZDMRJUS2US3JQJB5FVPYNAXDY2/events.json","paper":"https://pith.science/paper/ZDMRJUS2"},"agent_actions":{"view_html":"https://pith.science/pith/ZDMRJUS2US3JQJB5FVPYNAXDY2","download_json":"https://pith.science/pith/ZDMRJUS2US3JQJB5FVPYNAXDY2.json","view_paper":"https://pith.science/paper/ZDMRJUS2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.1706&json=true","fetch_graph":"https://pith.science/api/pith-number/ZDMRJUS2US3JQJB5FVPYNAXDY2/graph.json","fetch_events":"https://pith.science/api/pith-number/ZDMRJUS2US3JQJB5FVPYNAXDY2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZDMRJUS2US3JQJB5FVPYNAXDY2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZDMRJUS2US3JQJB5FVPYNAXDY2/action/storage_attestation","attest_author":"https://pith.science/pith/ZDMRJUS2US3JQJB5FVPYNAXDY2/action/author_attestation","sign_citation":"https://pith.science/pith/ZDMRJUS2US3JQJB5FVPYNAXDY2/action/citation_signature","submit_replication":"https://pith.science/pith/ZDMRJUS2US3JQJB5FVPYNAXDY2/action/replication_record"}},"created_at":"2026-05-18T02:49:31.885074+00:00","updated_at":"2026-05-18T02:49:31.885074+00:00"}