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We find explicit formulas for the $q$-series coefficients of $(1-q^2)(1-q^3)(1-q^4)(1-q^5)\\dots$ and $(1-q^3)(1-q^4)(1-q^5)(1-q^6)\\dots$. In doing so, we extend certain observations made by Sudler in 1964. We also discuss the classification of the products $(1-q)(1-q^2)\\dots (1-q^m)$ and some related series with respect to their absolute largest coefficients."},"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":"1705.07504","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-21T20:05:43Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"fed9147a2e4eb1e75c46a08883b8a6415677ddfdc72968f4e71fa9c4599ac6be","abstract_canon_sha256":"e101e4d4b0b232085d9b9104a738cac609bdbea10affb47e3ec86c2abd24488a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:06.579175Z","signature_b64":"LSvSQvLUwJAZ1sbfMaVddhzIZ07R9oEL6WhIMoEpYDhuw1zeX18mH9NfpCygsAUuS2FMUno3ugmcWyZPA+Q/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f3a79dad76513ea455164bcf94df7e472f467ab39ffe941cd133035eb74dd6d","last_reissued_at":"2026-05-18T00:33:06.578471Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:06.578471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On some polynomials and series of Bloch-Polya Type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Alexander Berkovich, Ali K. 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