{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:IWAKEDVZCQ7NMEKBAVU3HAU6V4","short_pith_number":"pith:IWAKEDVZ","schema_version":"1.0","canonical_sha256":"4580a20eb9143ed611410569b3829eaf3a2f161d0dc75dc4854841dbd512de1e","source":{"kind":"arxiv","id":"2307.15206","version":2},"attestation_state":"computed","paper":{"title":"Ramanujan-Shen's differential equations for Eisenstein series of level 2","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Masato Kobayashi","submitted_at":"2023-07-27T21:34:23Z","abstract_excerpt":"Ramanujan (1916) and Shen (1999) discovered differential equations for classical Eisenstein series. Motivated by them, we derive new differential equations for Eisenstein series of level 2 from the second kind of Jacobi theta function. This gives a new characterization of a system of differential equations by Ablowitz-Chakravarty-Hahn (2006), Hahn (2008), Kaneko-Koike (2003), Maier (2011) and Toh (2011). As application, we show some arithmetic results on Ramanujan's tau function."},"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":"2307.15206","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NT","submitted_at":"2023-07-27T21:34:23Z","cross_cats_sorted":[],"title_canon_sha256":"c30831797dc28b2780549a9d8152020ec1d7140881ea4cdbabbe8e7016b5262d","abstract_canon_sha256":"b3f76d6626aefab8a7c4f5db311a448c39326169298a0c4302d8b1fb9e68978f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:07:28.543245Z","signature_b64":"hoMs71q74Mixi7yyLjq5cKlwWpRu24nIpiWFV2laXgqdbKafZHO/Y1Zj4ht8wSLuO0/a7yQSlOb08gj5eVYgDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4580a20eb9143ed611410569b3829eaf3a2f161d0dc75dc4854841dbd512de1e","last_reissued_at":"2026-07-05T08:07:28.542763Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:07:28.542763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ramanujan-Shen's differential equations for Eisenstein series of level 2","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Masato Kobayashi","submitted_at":"2023-07-27T21:34:23Z","abstract_excerpt":"Ramanujan (1916) and Shen (1999) discovered differential equations for classical Eisenstein series. Motivated by them, we derive new differential equations for Eisenstein series of level 2 from the second kind of Jacobi theta function. This gives a new characterization of a system of differential equations by Ablowitz-Chakravarty-Hahn (2006), Hahn (2008), Kaneko-Koike (2003), Maier (2011) and Toh (2011). As application, we show some arithmetic results on Ramanujan's tau function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.15206","kind":"arxiv","version":2},"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/2307.15206/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":"2307.15206","created_at":"2026-07-05T08:07:28.542823+00:00"},{"alias_kind":"arxiv_version","alias_value":"2307.15206v2","created_at":"2026-07-05T08:07:28.542823+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.15206","created_at":"2026-07-05T08:07:28.542823+00:00"},{"alias_kind":"pith_short_12","alias_value":"IWAKEDVZCQ7N","created_at":"2026-07-05T08:07:28.542823+00:00"},{"alias_kind":"pith_short_16","alias_value":"IWAKEDVZCQ7NMEKB","created_at":"2026-07-05T08:07:28.542823+00:00"},{"alias_kind":"pith_short_8","alias_value":"IWAKEDVZ","created_at":"2026-07-05T08:07:28.542823+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/IWAKEDVZCQ7NMEKBAVU3HAU6V4","json":"https://pith.science/pith/IWAKEDVZCQ7NMEKBAVU3HAU6V4.json","graph_json":"https://pith.science/api/pith-number/IWAKEDVZCQ7NMEKBAVU3HAU6V4/graph.json","events_json":"https://pith.science/api/pith-number/IWAKEDVZCQ7NMEKBAVU3HAU6V4/events.json","paper":"https://pith.science/paper/IWAKEDVZ"},"agent_actions":{"view_html":"https://pith.science/pith/IWAKEDVZCQ7NMEKBAVU3HAU6V4","download_json":"https://pith.science/pith/IWAKEDVZCQ7NMEKBAVU3HAU6V4.json","view_paper":"https://pith.science/paper/IWAKEDVZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2307.15206&json=true","fetch_graph":"https://pith.science/api/pith-number/IWAKEDVZCQ7NMEKBAVU3HAU6V4/graph.json","fetch_events":"https://pith.science/api/pith-number/IWAKEDVZCQ7NMEKBAVU3HAU6V4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IWAKEDVZCQ7NMEKBAVU3HAU6V4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IWAKEDVZCQ7NMEKBAVU3HAU6V4/action/storage_attestation","attest_author":"https://pith.science/pith/IWAKEDVZCQ7NMEKBAVU3HAU6V4/action/author_attestation","sign_citation":"https://pith.science/pith/IWAKEDVZCQ7NMEKBAVU3HAU6V4/action/citation_signature","submit_replication":"https://pith.science/pith/IWAKEDVZCQ7NMEKBAVU3HAU6V4/action/replication_record"}},"created_at":"2026-07-05T08:07:28.542823+00:00","updated_at":"2026-07-05T08:07:28.542823+00:00"}