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Under hypotheses on the roots of $f-f(0)$, we use the Hardy--Littlewood circle method, a polylogarithm identity, and the Matsumoto--Weng zeta function to derive asymptotic formulae for $p_{\\mathcal{A}_f}(n)$ as $n$ tends to infinity. This generalises asymptotic formulae for the number of partitions into perfect $d$th powers, established by Vaughan for $d=2$, and Gafni "},"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":"1705.00384","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-30T23:10:39Z","cross_cats_sorted":[],"title_canon_sha256":"922c247adf9b9fe7186fb30f3a82a8101fe9d98bf618fbc6c847e6b7ca6fdee8","abstract_canon_sha256":"e38f9fca83a3ee87c2f331debaa1a5d2014366bbbccfdfe3f9781b8e361350b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:04.134120Z","signature_b64":"YfmukjUhSbtratXJHVsCG0BZ2sUyuI6N7KH4LlvKmGUwb3xOvMnz7yGsl5ez1webMm+OP7pN8tKt+hv8AyTQBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89cf6c02b37429f032bcca4852c86222f1a4f1bfc770f07b205fc9b7020c9f65","last_reissued_at":"2026-05-18T00:18:04.133643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:04.133643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polynomial partition asymptotics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexander Dunn, Nicolas Robles","submitted_at":"2017-04-30T23:10:39Z","abstract_excerpt":"Let $f \\in \\mathbb{Z}[y]$ be a polynomial such that $f(\\mathbb{N}) \\subseteq \\mathbb{N}$, and let $p_{\\mathcal{A}_{f}}(n)$ denote number of partitions of $n$ whose parts lie in the set $\\mathcal{A}_f:=\\{f(n):n \\in \\mathbb{N}\\}$. Under hypotheses on the roots of $f-f(0)$, we use the Hardy--Littlewood circle method, a polylogarithm identity, and the Matsumoto--Weng zeta function to derive asymptotic formulae for $p_{\\mathcal{A}_f}(n)$ as $n$ tends to infinity. 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