{"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"}