{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2EJROZRB6Z5ZRA6LHNYLHFMGBH","short_pith_number":"pith:2EJROZRB","schema_version":"1.0","canonical_sha256":"d113176621f67b9883cb3b70b3958609fc92c2f934e96b2ac3f12d43462d4144","source":{"kind":"arxiv","id":"1702.01249","version":2},"attestation_state":"computed","paper":{"title":"On the number of representations of certain quadratic forms and a formula for the Ramanujan Tau function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anup Kumar Singh, B. Ramakrishnan, Brundaban Sahu","submitted_at":"2017-02-04T07:22:45Z","abstract_excerpt":"In this paper, we find the number of representations of the quadratic form $x_1^2+ x_1x_2 + x_2^2 + \\ldots + x_{2k-1}^2 + x_{2k-1}x_{2k} + x_{2k}^2,$ for $k=7,9,11,12,14$ using the theory of modular forms. By comparing our formulas with the formulas obtained by G. A. Lomadze, we obtain the Fourier coefficients of certain newforms of level $3$ and weights $7,9,11$ in terms of certain finite sums involving the solutions of similar quadratic forms of lower variables. In the case of $24$ variables, comparison of these formulas gives rise to a new formula for the Ramanujan 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":"1702.01249","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-04T07:22:45Z","cross_cats_sorted":[],"title_canon_sha256":"c35f5cb568d046997e82010e0bd5f28f803f149000f55900c81a2e403417c41a","abstract_canon_sha256":"65ec830ca3187f282b00b6fd66245723c5a23a897f6acffa05d2ae53d7376310"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:36.046804Z","signature_b64":"zw1Rj8uJOsAcIA6iGoxm9F6l0tAkMYBvgjQYubLjdwBVo1rV5aydF0va58b26eLZ4aDyQriNFL0HSUMHAzYqAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d113176621f67b9883cb3b70b3958609fc92c2f934e96b2ac3f12d43462d4144","last_reissued_at":"2026-05-18T00:38:36.046274Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:36.046274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the number of representations of certain quadratic forms and a formula for the Ramanujan Tau function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anup Kumar Singh, B. Ramakrishnan, Brundaban Sahu","submitted_at":"2017-02-04T07:22:45Z","abstract_excerpt":"In this paper, we find the number of representations of the quadratic form $x_1^2+ x_1x_2 + x_2^2 + \\ldots + x_{2k-1}^2 + x_{2k-1}x_{2k} + x_{2k}^2,$ for $k=7,9,11,12,14$ using the theory of modular forms. By comparing our formulas with the formulas obtained by G. A. Lomadze, we obtain the Fourier coefficients of certain newforms of level $3$ and weights $7,9,11$ in terms of certain finite sums involving the solutions of similar quadratic forms of lower variables. In the case of $24$ variables, comparison of these formulas gives rise to a new formula for the Ramanujan Tau function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01249","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":""},"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":"1702.01249","created_at":"2026-05-18T00:38:36.046371+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.01249v2","created_at":"2026-05-18T00:38:36.046371+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01249","created_at":"2026-05-18T00:38:36.046371+00:00"},{"alias_kind":"pith_short_12","alias_value":"2EJROZRB6Z5Z","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2EJROZRB6Z5ZRA6L","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2EJROZRB","created_at":"2026-05-18T12:30:55.937587+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/2EJROZRB6Z5ZRA6LHNYLHFMGBH","json":"https://pith.science/pith/2EJROZRB6Z5ZRA6LHNYLHFMGBH.json","graph_json":"https://pith.science/api/pith-number/2EJROZRB6Z5ZRA6LHNYLHFMGBH/graph.json","events_json":"https://pith.science/api/pith-number/2EJROZRB6Z5ZRA6LHNYLHFMGBH/events.json","paper":"https://pith.science/paper/2EJROZRB"},"agent_actions":{"view_html":"https://pith.science/pith/2EJROZRB6Z5ZRA6LHNYLHFMGBH","download_json":"https://pith.science/pith/2EJROZRB6Z5ZRA6LHNYLHFMGBH.json","view_paper":"https://pith.science/paper/2EJROZRB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.01249&json=true","fetch_graph":"https://pith.science/api/pith-number/2EJROZRB6Z5ZRA6LHNYLHFMGBH/graph.json","fetch_events":"https://pith.science/api/pith-number/2EJROZRB6Z5ZRA6LHNYLHFMGBH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2EJROZRB6Z5ZRA6LHNYLHFMGBH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2EJROZRB6Z5ZRA6LHNYLHFMGBH/action/storage_attestation","attest_author":"https://pith.science/pith/2EJROZRB6Z5ZRA6LHNYLHFMGBH/action/author_attestation","sign_citation":"https://pith.science/pith/2EJROZRB6Z5ZRA6LHNYLHFMGBH/action/citation_signature","submit_replication":"https://pith.science/pith/2EJROZRB6Z5ZRA6LHNYLHFMGBH/action/replication_record"}},"created_at":"2026-05-18T00:38:36.046371+00:00","updated_at":"2026-05-18T00:38:36.046371+00:00"}