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We revisit a family of such functions, denoted $Q_k$, and study the $p$-adic properties of their $q$-brackets. To do this, we define regularized versions $Q_k^{(p)}$ for primes $p.$ We also use Jacobi forms to show that the $\\left<Q_k^{(p)}\\right>_q$ are quasimodular and find explicit expressions for them in terms of the $\\left<Q_k\\right>_q$."},"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":"1509.07161","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-23T21:11:26Z","cross_cats_sorted":[],"title_canon_sha256":"b2cb1056e01800895b80d0cf2bf98d3d28b9f085cd07f627bcf476b121555b70","abstract_canon_sha256":"41d58535b7fb442c2999dfbfbe7421f23cac8b7ff8a4043a419d37310c99d046"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:59.971568Z","signature_b64":"qloY1iO0h5P7HSILhPTCllQkkTQStyGoxkhkobatliHr1FC5ODTSUsrfUpr8G2ICUoU0ikonRd0W0Sa4flu6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f602be670332029c7b17ec4df9195d8b0fc80cbd2c4c8624c4b93741e1bb854","last_reissued_at":"2026-05-18T01:26:59.970903Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:59.970903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On p-adic modular forms and the Bloch-Okounkov theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Marie Jameson, Michael Griffin, Sarah Trebat-Leder","submitted_at":"2015-09-23T21:11:26Z","abstract_excerpt":"Bloch-Okounkov studied certain functions on partitions $f$ called shifted symmetric polynomials. 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