{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:WEKOBZIHL3I4DLMAK3QFIPAIBD","short_pith_number":"pith:WEKOBZIH","schema_version":"1.0","canonical_sha256":"b114e0e5075ed1c1ad8056e0543c0808f75e96921774d8813e3742c488320ad0","source":{"kind":"arxiv","id":"1201.6538","version":1},"attestation_state":"computed","paper":{"title":"On A Rapidly Converging Series For The Riemann Zeta Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.NT","authors_text":"Alois Pichler","submitted_at":"2012-01-31T13:54:53Z","abstract_excerpt":"To evaluate Riemann's zeta function is important for many investigations related to the area of number theory, and to have quickly converging series at hand in particular. We investigate a class of summation formulae and find, as a special case, a new proof of a rapidly converging series for the Riemann zeta function. The series converges in the entire complex plane, its rate of convergence being significantly faster than comparable representations, and so is a useful basis for evaluation algorithms. The evaluation of corresponding coefficients is not problematic, and precise convergence rates"},"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":"1201.6538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-01-31T13:54:53Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4c9eeaaf8b371bdaa01e026a9313b82c45dd8c06bfe3e70b9cddd3d7de424fd6","abstract_canon_sha256":"a0ab15ae3172547a347684f5e7072407fd900feca763a4175af86bc50d758abb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:31.233838Z","signature_b64":"StGXNgb5KHxdgFuf353Xao9+Vd6EsodLz/+jRFW0mTSGc/5u/OlxWAx1+NtxymuraPYNaVuP1dzFrOqIk5wjAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b114e0e5075ed1c1ad8056e0543c0808f75e96921774d8813e3742c488320ad0","last_reissued_at":"2026-05-18T04:03:31.233303Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:31.233303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On A Rapidly Converging Series For The Riemann Zeta Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.NT","authors_text":"Alois Pichler","submitted_at":"2012-01-31T13:54:53Z","abstract_excerpt":"To evaluate Riemann's zeta function is important for many investigations related to the area of number theory, and to have quickly converging series at hand in particular. We investigate a class of summation formulae and find, as a special case, a new proof of a rapidly converging series for the Riemann zeta function. The series converges in the entire complex plane, its rate of convergence being significantly faster than comparable representations, and so is a useful basis for evaluation algorithms. The evaluation of corresponding coefficients is not problematic, and precise convergence rates"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6538","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":"1201.6538","created_at":"2026-05-18T04:03:31.233393+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.6538v1","created_at":"2026-05-18T04:03:31.233393+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.6538","created_at":"2026-05-18T04:03:31.233393+00:00"},{"alias_kind":"pith_short_12","alias_value":"WEKOBZIHL3I4","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"WEKOBZIHL3I4DLMA","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"WEKOBZIH","created_at":"2026-05-18T12:27:25.539911+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/WEKOBZIHL3I4DLMAK3QFIPAIBD","json":"https://pith.science/pith/WEKOBZIHL3I4DLMAK3QFIPAIBD.json","graph_json":"https://pith.science/api/pith-number/WEKOBZIHL3I4DLMAK3QFIPAIBD/graph.json","events_json":"https://pith.science/api/pith-number/WEKOBZIHL3I4DLMAK3QFIPAIBD/events.json","paper":"https://pith.science/paper/WEKOBZIH"},"agent_actions":{"view_html":"https://pith.science/pith/WEKOBZIHL3I4DLMAK3QFIPAIBD","download_json":"https://pith.science/pith/WEKOBZIHL3I4DLMAK3QFIPAIBD.json","view_paper":"https://pith.science/paper/WEKOBZIH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.6538&json=true","fetch_graph":"https://pith.science/api/pith-number/WEKOBZIHL3I4DLMAK3QFIPAIBD/graph.json","fetch_events":"https://pith.science/api/pith-number/WEKOBZIHL3I4DLMAK3QFIPAIBD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WEKOBZIHL3I4DLMAK3QFIPAIBD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WEKOBZIHL3I4DLMAK3QFIPAIBD/action/storage_attestation","attest_author":"https://pith.science/pith/WEKOBZIHL3I4DLMAK3QFIPAIBD/action/author_attestation","sign_citation":"https://pith.science/pith/WEKOBZIHL3I4DLMAK3QFIPAIBD/action/citation_signature","submit_replication":"https://pith.science/pith/WEKOBZIHL3I4DLMAK3QFIPAIBD/action/replication_record"}},"created_at":"2026-05-18T04:03:31.233393+00:00","updated_at":"2026-05-18T04:03:31.233393+00:00"}