{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:2UZUMRTA6V5C4SQZMS5A52AWHO","short_pith_number":"pith:2UZUMRTA","schema_version":"1.0","canonical_sha256":"d533464660f57a2e4a1964ba0ee8163ba5d215f4ae0b1b62ae68569208370fea","source":{"kind":"arxiv","id":"2308.08988","version":2},"attestation_state":"computed","paper":{"title":"A Dirichlet character analogue of Ramanujan's formula for odd zeta values","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anushree Gupta, Bibekananda Maji, Md Kashif Jamal, Nilmoni Karak","submitted_at":"2023-08-17T13:49:37Z","abstract_excerpt":"In 2001, Kanemitsu, Tanigawa, and Yoshimoto studied the following generalized Lambert series, $$\n  \\sum_{n=1}^{\\infty} \\frac{n^{N-2h} }{\\exp(n^N x)-1},\n  $$ for $N \\in \\mathbb{N}$ and $h\\in \\mathbb{Z}$ with some restriction on $h$. Recently, Dixit and the last author pointed out that this series has already been present in the Lost Notebook of Ramanujan with a more general form. Although, Ramanujan did not provide any transformation identity for it. In the same paper, Dixit and the last author found an elegant generalization of Ramanujan's celebrated identity for $\\zeta(2m+1)$ while extending "},"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":"2308.08988","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-08-17T13:49:37Z","cross_cats_sorted":[],"title_canon_sha256":"f6752de8fd773a9a332d978a1856114fc0edd4fd87ce79d1fabc97343df30921","abstract_canon_sha256":"a874ffde41fe5121b965fcf2f2b4fd11001051e568f39995edfa672bc622df35"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:55:24.667989Z","signature_b64":"F976AtaOEH4sG5jd0qgj9j7F3z132MZc5jeLF5iJrY0H5pIYPcZqZfKJUyPLyaGjNwSlWY5lFXzu0AVWzV8qCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d533464660f57a2e4a1964ba0ee8163ba5d215f4ae0b1b62ae68569208370fea","last_reissued_at":"2026-07-05T06:55:24.667520Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:55:24.667520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Dirichlet character analogue of Ramanujan's formula for odd zeta values","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anushree Gupta, Bibekananda Maji, Md Kashif Jamal, Nilmoni Karak","submitted_at":"2023-08-17T13:49:37Z","abstract_excerpt":"In 2001, Kanemitsu, Tanigawa, and Yoshimoto studied the following generalized Lambert series, $$\n  \\sum_{n=1}^{\\infty} \\frac{n^{N-2h} }{\\exp(n^N x)-1},\n  $$ for $N \\in \\mathbb{N}$ and $h\\in \\mathbb{Z}$ with some restriction on $h$. Recently, Dixit and the last author pointed out that this series has already been present in the Lost Notebook of Ramanujan with a more general form. Although, Ramanujan did not provide any transformation identity for it. In the same paper, Dixit and the last author found an elegant generalization of Ramanujan's celebrated identity for $\\zeta(2m+1)$ while extending "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.08988","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/2308.08988/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":"2308.08988","created_at":"2026-07-05T06:55:24.667579+00:00"},{"alias_kind":"arxiv_version","alias_value":"2308.08988v2","created_at":"2026-07-05T06:55:24.667579+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.08988","created_at":"2026-07-05T06:55:24.667579+00:00"},{"alias_kind":"pith_short_12","alias_value":"2UZUMRTA6V5C","created_at":"2026-07-05T06:55:24.667579+00:00"},{"alias_kind":"pith_short_16","alias_value":"2UZUMRTA6V5C4SQZ","created_at":"2026-07-05T06:55:24.667579+00:00"},{"alias_kind":"pith_short_8","alias_value":"2UZUMRTA","created_at":"2026-07-05T06:55:24.667579+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/2UZUMRTA6V5C4SQZMS5A52AWHO","json":"https://pith.science/pith/2UZUMRTA6V5C4SQZMS5A52AWHO.json","graph_json":"https://pith.science/api/pith-number/2UZUMRTA6V5C4SQZMS5A52AWHO/graph.json","events_json":"https://pith.science/api/pith-number/2UZUMRTA6V5C4SQZMS5A52AWHO/events.json","paper":"https://pith.science/paper/2UZUMRTA"},"agent_actions":{"view_html":"https://pith.science/pith/2UZUMRTA6V5C4SQZMS5A52AWHO","download_json":"https://pith.science/pith/2UZUMRTA6V5C4SQZMS5A52AWHO.json","view_paper":"https://pith.science/paper/2UZUMRTA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2308.08988&json=true","fetch_graph":"https://pith.science/api/pith-number/2UZUMRTA6V5C4SQZMS5A52AWHO/graph.json","fetch_events":"https://pith.science/api/pith-number/2UZUMRTA6V5C4SQZMS5A52AWHO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2UZUMRTA6V5C4SQZMS5A52AWHO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2UZUMRTA6V5C4SQZMS5A52AWHO/action/storage_attestation","attest_author":"https://pith.science/pith/2UZUMRTA6V5C4SQZMS5A52AWHO/action/author_attestation","sign_citation":"https://pith.science/pith/2UZUMRTA6V5C4SQZMS5A52AWHO/action/citation_signature","submit_replication":"https://pith.science/pith/2UZUMRTA6V5C4SQZMS5A52AWHO/action/replication_record"}},"created_at":"2026-07-05T06:55:24.667579+00:00","updated_at":"2026-07-05T06:55:24.667579+00:00"}