{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:WWXRSMNDRIZ3AR6SFBVGMYKZYP","short_pith_number":"pith:WWXRSMND","schema_version":"1.0","canonical_sha256":"b5af1931a38a33b047d2286a666159c3db7705cb46bd9700091dca06df0f8ef2","source":{"kind":"arxiv","id":"math/0607247","version":5},"attestation_state":"computed","paper":{"title":"A detailed note on the zeros of Eisenstein series for $\\Gamma_0^* (5)$ and $\\Gamma_0^* (7)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Junichi Shigezumi","submitted_at":"2006-07-11T06:27:55Z","abstract_excerpt":"The present paper provides the details omitted from the more concise study \"On the zeros of Eisenstein series for $\\Gamma_0^* (5)$ and $\\Gamma_0^* (7)$.\"\n  We locate almost all of the zeros of the Eisenstein series associated with the Fricke groups of level 5 and 7 in their fundamental domains by applying and extending the method of F. K. C. Rankin and H. P. F. Swinnerton-Dyer (1970). We also use the arguments of some terms of the Eisenstein series in order to improve existing error bounds."},"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":"math/0607247","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2006-07-11T06:27:55Z","cross_cats_sorted":[],"title_canon_sha256":"5f95499b7d34c5ac51b1aaac0a66722819d24f8bf06f539ae974b4ac05093133","abstract_canon_sha256":"c849077a9cfc21a970b021cf13f91362cbe42337cec3c6c24c36b2b317924361"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:12.959946Z","signature_b64":"X6IdJxjmFLQcY+ltdpFYlNOHrRrzcXtlnHoYlsubBot/7Gj+wsSEEpcc23Qyas19fmLpGSlG//SWcsLOZgR0AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5af1931a38a33b047d2286a666159c3db7705cb46bd9700091dca06df0f8ef2","last_reissued_at":"2026-05-18T02:56:12.959522Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:12.959522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A detailed note on the zeros of Eisenstein series for $\\Gamma_0^* (5)$ and $\\Gamma_0^* (7)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Junichi Shigezumi","submitted_at":"2006-07-11T06:27:55Z","abstract_excerpt":"The present paper provides the details omitted from the more concise study \"On the zeros of Eisenstein series for $\\Gamma_0^* (5)$ and $\\Gamma_0^* (7)$.\"\n  We locate almost all of the zeros of the Eisenstein series associated with the Fricke groups of level 5 and 7 in their fundamental domains by applying and extending the method of F. K. C. Rankin and H. P. F. Swinnerton-Dyer (1970). We also use the arguments of some terms of the Eisenstein series in order to improve existing error bounds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607247","kind":"arxiv","version":5},"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":"math/0607247","created_at":"2026-05-18T02:56:12.959575+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0607247v5","created_at":"2026-05-18T02:56:12.959575+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0607247","created_at":"2026-05-18T02:56:12.959575+00:00"},{"alias_kind":"pith_short_12","alias_value":"WWXRSMNDRIZ3","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"WWXRSMNDRIZ3AR6S","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"WWXRSMND","created_at":"2026-05-18T12:25:54.717736+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/WWXRSMNDRIZ3AR6SFBVGMYKZYP","json":"https://pith.science/pith/WWXRSMNDRIZ3AR6SFBVGMYKZYP.json","graph_json":"https://pith.science/api/pith-number/WWXRSMNDRIZ3AR6SFBVGMYKZYP/graph.json","events_json":"https://pith.science/api/pith-number/WWXRSMNDRIZ3AR6SFBVGMYKZYP/events.json","paper":"https://pith.science/paper/WWXRSMND"},"agent_actions":{"view_html":"https://pith.science/pith/WWXRSMNDRIZ3AR6SFBVGMYKZYP","download_json":"https://pith.science/pith/WWXRSMNDRIZ3AR6SFBVGMYKZYP.json","view_paper":"https://pith.science/paper/WWXRSMND","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0607247&json=true","fetch_graph":"https://pith.science/api/pith-number/WWXRSMNDRIZ3AR6SFBVGMYKZYP/graph.json","fetch_events":"https://pith.science/api/pith-number/WWXRSMNDRIZ3AR6SFBVGMYKZYP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WWXRSMNDRIZ3AR6SFBVGMYKZYP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WWXRSMNDRIZ3AR6SFBVGMYKZYP/action/storage_attestation","attest_author":"https://pith.science/pith/WWXRSMNDRIZ3AR6SFBVGMYKZYP/action/author_attestation","sign_citation":"https://pith.science/pith/WWXRSMNDRIZ3AR6SFBVGMYKZYP/action/citation_signature","submit_replication":"https://pith.science/pith/WWXRSMNDRIZ3AR6SFBVGMYKZYP/action/replication_record"}},"created_at":"2026-05-18T02:56:12.959575+00:00","updated_at":"2026-05-18T02:56:12.959575+00:00"}