{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:XJAWFOUM6U55I2R3F3FI32XOY3","short_pith_number":"pith:XJAWFOUM","schema_version":"1.0","canonical_sha256":"ba4162ba8cf53bd46a3b2eca8deaeec6f154d6f89fbdf8f96704de9538d230e1","source":{"kind":"arxiv","id":"1908.07737","version":1},"attestation_state":"computed","paper":{"title":"Some results on vanishing coefficients in infinite product expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mandeep Kaur, Nayandeep Deka Baruah","submitted_at":"2019-08-21T07:48:48Z","abstract_excerpt":"Recently, M. D. Hirschhorn proved that, if $\\sum_{n=0}^\\infty a_nq^n := (-q,-q^4;q^5)_\\infty(q,q^9;q^{10})_\\infty^3$ and $\\sum_{n=0}^\\infty b_nq^n:=(-q^2,-q^3;q^5)_\\infty(q^3,q^7;q^{10})_\\infty^3$, then $a_{5n+2}=a_{5n+4}=0$ and $b_{5n+1}=b_{5n+4}=0$. Motivated by the work of Hirschhorn, D. Tang proved some comparable results including the following: If $ \\sum_{n=0}^\\infty c_nq^n := (-q,-q^4;q^5)_\\infty^3(q^3,q^7;q^{10})_\\infty$ and $\\sum_{n=0}^\\infty d_nq^n := (-q^2,-q^3;q^5)_\\infty^3(q,q^9;q^{10})_\\infty$, then $c_{5n+3}=c_{5n+4}=0$ and $d_{5n+3}=d_{5n+4}=0$.\n  In this paper, we prove that $"},"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":"1908.07737","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-08-21T07:48:48Z","cross_cats_sorted":[],"title_canon_sha256":"a3d85157e020ab31d164de766c00d4a8dd80a6b18e26061d552ec3ff93c78985","abstract_canon_sha256":"fe6dc6a693d7aa45d9c391020148bdcf095322050420ec33601137f13e3184ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:36:13.323349Z","signature_b64":"KCEtp41ZDCHHmiKEXqP6wBn+AL/kf8sJ4DA9iDWjg3HSTGp6xn/KZHVqbG2vqTx8sib8DmYyCvZ5HltH5msKCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba4162ba8cf53bd46a3b2eca8deaeec6f154d6f89fbdf8f96704de9538d230e1","last_reissued_at":"2026-07-05T05:36:13.322942Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:36:13.322942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some results on vanishing coefficients in infinite product expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mandeep Kaur, Nayandeep Deka Baruah","submitted_at":"2019-08-21T07:48:48Z","abstract_excerpt":"Recently, M. D. Hirschhorn proved that, if $\\sum_{n=0}^\\infty a_nq^n := (-q,-q^4;q^5)_\\infty(q,q^9;q^{10})_\\infty^3$ and $\\sum_{n=0}^\\infty b_nq^n:=(-q^2,-q^3;q^5)_\\infty(q^3,q^7;q^{10})_\\infty^3$, then $a_{5n+2}=a_{5n+4}=0$ and $b_{5n+1}=b_{5n+4}=0$. Motivated by the work of Hirschhorn, D. Tang proved some comparable results including the following: If $ \\sum_{n=0}^\\infty c_nq^n := (-q,-q^4;q^5)_\\infty^3(q^3,q^7;q^{10})_\\infty$ and $\\sum_{n=0}^\\infty d_nq^n := (-q^2,-q^3;q^5)_\\infty^3(q,q^9;q^{10})_\\infty$, then $c_{5n+3}=c_{5n+4}=0$ and $d_{5n+3}=d_{5n+4}=0$.\n  In this paper, we prove that $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07737","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.07737/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":"1908.07737","created_at":"2026-07-05T05:36:13.322993+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.07737v1","created_at":"2026-07-05T05:36:13.322993+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07737","created_at":"2026-07-05T05:36:13.322993+00:00"},{"alias_kind":"pith_short_12","alias_value":"XJAWFOUM6U55","created_at":"2026-07-05T05:36:13.322993+00:00"},{"alias_kind":"pith_short_16","alias_value":"XJAWFOUM6U55I2R3","created_at":"2026-07-05T05:36:13.322993+00:00"},{"alias_kind":"pith_short_8","alias_value":"XJAWFOUM","created_at":"2026-07-05T05:36:13.322993+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/XJAWFOUM6U55I2R3F3FI32XOY3","json":"https://pith.science/pith/XJAWFOUM6U55I2R3F3FI32XOY3.json","graph_json":"https://pith.science/api/pith-number/XJAWFOUM6U55I2R3F3FI32XOY3/graph.json","events_json":"https://pith.science/api/pith-number/XJAWFOUM6U55I2R3F3FI32XOY3/events.json","paper":"https://pith.science/paper/XJAWFOUM"},"agent_actions":{"view_html":"https://pith.science/pith/XJAWFOUM6U55I2R3F3FI32XOY3","download_json":"https://pith.science/pith/XJAWFOUM6U55I2R3F3FI32XOY3.json","view_paper":"https://pith.science/paper/XJAWFOUM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.07737&json=true","fetch_graph":"https://pith.science/api/pith-number/XJAWFOUM6U55I2R3F3FI32XOY3/graph.json","fetch_events":"https://pith.science/api/pith-number/XJAWFOUM6U55I2R3F3FI32XOY3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XJAWFOUM6U55I2R3F3FI32XOY3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XJAWFOUM6U55I2R3F3FI32XOY3/action/storage_attestation","attest_author":"https://pith.science/pith/XJAWFOUM6U55I2R3F3FI32XOY3/action/author_attestation","sign_citation":"https://pith.science/pith/XJAWFOUM6U55I2R3F3FI32XOY3/action/citation_signature","submit_replication":"https://pith.science/pith/XJAWFOUM6U55I2R3F3FI32XOY3/action/replication_record"}},"created_at":"2026-07-05T05:36:13.322993+00:00","updated_at":"2026-07-05T05:36:13.322993+00:00"}