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In particular, for the partition function $p(n)$, they prove that \\[p(n)=\\frac{1}{24n-1} \\sum P(\\alpha_Q),\\] where $P$ is a weak Maass form and $\\alpha_Q$ ranges over a finite set of discriminant $-24n+1$ CM points. Moreover, they show that $6 (24n-1) P(\\alpha_Q)$ is always an algebraic integer, and they conjecture that $(24n-1) P(\\alpha_Q)$ is always an algebraic integer. Here we prove a general theorem which implies this conjecture as"},"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":"1107.4114","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-07-20T20:27:38Z","cross_cats_sorted":[],"title_canon_sha256":"55a27dd631dfb0078bc48c0fb405cfe6f132688a2461defb4e02d9824cc159e0","abstract_canon_sha256":"fef51953ace8108024dac748a124857f8ffef4c2b9a8daaa36e31c98083d47e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:13.205941Z","signature_b64":"+LOeqti9o+TuZd+mFIl7/JpmyU/jJjeefUIXvsNsJjyUt7k6mMG8qXTE0Zp6picXerS/sGNO0RFFvBmtXCl3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adf66f0a9746e2fab8bb3e99e3694595507a68d01d693d03a848160af9579a68","last_reissued_at":"2026-05-18T04:17:13.205292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:13.205292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integrality Properties of the CM-values of Certain Weak Maass Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eric Larson, Larry Rolen","submitted_at":"2011-07-20T20:27:38Z","abstract_excerpt":"In a recent paper, Bruinier and Ono prove that the coefficients of certain weight -1/2 harmonic Maass forms are traces of singular moduli for weak Maass forms. In particular, for the partition function $p(n)$, they prove that \\[p(n)=\\frac{1}{24n-1} \\sum P(\\alpha_Q),\\] where $P$ is a weak Maass form and $\\alpha_Q$ ranges over a finite set of discriminant $-24n+1$ CM points. Moreover, they show that $6 (24n-1) P(\\alpha_Q)$ is always an algebraic integer, and they conjecture that $(24n-1) P(\\alpha_Q)$ is always an algebraic integer. 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