{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:XSLL4COMZ3FNBW67RFRUZSP3ZB","short_pith_number":"pith:XSLL4COM","schema_version":"1.0","canonical_sha256":"bc96be09cccecad0dbdf89634cc9fbc84b7ebc264056fed3966d262a37e31c3e","source":{"kind":"arxiv","id":"1502.05679","version":4},"attestation_state":"computed","paper":{"title":"Explicit estimates for the zeros of Hecke $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Asif Zaman","submitted_at":"2015-02-19T19:47:31Z","abstract_excerpt":"Let $K$ be a number field and, for an integral ideal $\\mathfrak{q}$ of $K$, let $\\chi$ be a character of the narrow ray class group modulo $\\mathfrak{q}$. We establish various new and improved explicit results, with effective dependence on $K$, $\\mathfrak{q}$ and $\\chi$, regarding the zeros of the Hecke L-function $L(s,\\chi)$, such as zero-free regions, Deuring-Heilbronn phenomenon, and zero density estimates."},"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":"1502.05679","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-19T19:47:31Z","cross_cats_sorted":[],"title_canon_sha256":"0aa1e0e074dcb4a90a92de76b85d148bf42102c9fa8fb608808db50f8df91bb5","abstract_canon_sha256":"55650b3e095e9cbb69f3cf3304139dbf601c35d2f9a0fb09f923c021b89cf5d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:10.040921Z","signature_b64":"y3mpu6BPH1nbunVmlj9FoJzMl6aCJByCIQDu4gQm1EktaCKin/i/EhnvjQw3d6vaLQP4nsm+uh5GQjtivnpgBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc96be09cccecad0dbdf89634cc9fbc84b7ebc264056fed3966d262a37e31c3e","last_reissued_at":"2026-05-18T01:18:10.040367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:10.040367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit estimates for the zeros of Hecke $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Asif Zaman","submitted_at":"2015-02-19T19:47:31Z","abstract_excerpt":"Let $K$ be a number field and, for an integral ideal $\\mathfrak{q}$ of $K$, let $\\chi$ be a character of the narrow ray class group modulo $\\mathfrak{q}$. We establish various new and improved explicit results, with effective dependence on $K$, $\\mathfrak{q}$ and $\\chi$, regarding the zeros of the Hecke L-function $L(s,\\chi)$, such as zero-free regions, Deuring-Heilbronn phenomenon, and zero density estimates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05679","kind":"arxiv","version":4},"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":"1502.05679","created_at":"2026-05-18T01:18:10.040440+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.05679v4","created_at":"2026-05-18T01:18:10.040440+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05679","created_at":"2026-05-18T01:18:10.040440+00:00"},{"alias_kind":"pith_short_12","alias_value":"XSLL4COMZ3FN","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XSLL4COMZ3FNBW67","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XSLL4COM","created_at":"2026-05-18T12:29:50.041715+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/XSLL4COMZ3FNBW67RFRUZSP3ZB","json":"https://pith.science/pith/XSLL4COMZ3FNBW67RFRUZSP3ZB.json","graph_json":"https://pith.science/api/pith-number/XSLL4COMZ3FNBW67RFRUZSP3ZB/graph.json","events_json":"https://pith.science/api/pith-number/XSLL4COMZ3FNBW67RFRUZSP3ZB/events.json","paper":"https://pith.science/paper/XSLL4COM"},"agent_actions":{"view_html":"https://pith.science/pith/XSLL4COMZ3FNBW67RFRUZSP3ZB","download_json":"https://pith.science/pith/XSLL4COMZ3FNBW67RFRUZSP3ZB.json","view_paper":"https://pith.science/paper/XSLL4COM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.05679&json=true","fetch_graph":"https://pith.science/api/pith-number/XSLL4COMZ3FNBW67RFRUZSP3ZB/graph.json","fetch_events":"https://pith.science/api/pith-number/XSLL4COMZ3FNBW67RFRUZSP3ZB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XSLL4COMZ3FNBW67RFRUZSP3ZB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XSLL4COMZ3FNBW67RFRUZSP3ZB/action/storage_attestation","attest_author":"https://pith.science/pith/XSLL4COMZ3FNBW67RFRUZSP3ZB/action/author_attestation","sign_citation":"https://pith.science/pith/XSLL4COMZ3FNBW67RFRUZSP3ZB/action/citation_signature","submit_replication":"https://pith.science/pith/XSLL4COMZ3FNBW67RFRUZSP3ZB/action/replication_record"}},"created_at":"2026-05-18T01:18:10.040440+00:00","updated_at":"2026-05-18T01:18:10.040440+00:00"}