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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 $","authors_text":"Mandeep Kaur, Nayandeep Deka Baruah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-08-21T07:48:48Z","title":"Some results on vanishing coefficients in infinite product expansions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07737","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2840887edb6b99fbef219055274096e2461424d36b190814be1e46a375e93365","target":"record","created_at":"2026-07-05T05:36:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fe6dc6a693d7aa45d9c391020148bdcf095322050420ec33601137f13e3184ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-08-21T07:48:48Z","title_canon_sha256":"a3d85157e020ab31d164de766c00d4a8dd80a6b18e26061d552ec3ff93c78985"},"schema_version":"1.0","source":{"id":"1908.07737","kind":"arxiv","version":1}},"canonical_sha256":"ba4162ba8cf53bd46a3b2eca8deaeec6f154d6f89fbdf8f96704de9538d230e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba4162ba8cf53bd46a3b2eca8deaeec6f154d6f89fbdf8f96704de9538d230e1","first_computed_at":"2026-07-05T05:36:13.322942Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:36:13.322942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KCEtp41ZDCHHmiKEXqP6wBn+AL/kf8sJ4DA9iDWjg3HSTGp6xn/KZHVqbG2vqTx8sib8DmYyCvZ5HltH5msKCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:36:13.323349Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07737","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2840887edb6b99fbef219055274096e2461424d36b190814be1e46a375e93365","sha256:60ba922e2039418d88adea8fcb752ad9b542172e00122f60c518cde03937a1bf"],"state_sha256":"8f4a2ff4fd2c37f799a0adc76a4ce8a033f13ef38b7770da9cfbc4be07a3d9a4"}