{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:R5QCXZTQGMQCTR5RP3CN7EMV3C","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"41d58535b7fb442c2999dfbfbe7421f23cac8b7ff8a4043a419d37310c99d046","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-23T21:11:26Z","title_canon_sha256":"b2cb1056e01800895b80d0cf2bf98d3d28b9f085cd07f627bcf476b121555b70"},"schema_version":"1.0","source":{"id":"1509.07161","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07161","created_at":"2026-05-18T01:26:59Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07161v2","created_at":"2026-05-18T01:26:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07161","created_at":"2026-05-18T01:26:59Z"},{"alias_kind":"pith_short_12","alias_value":"R5QCXZTQGMQC","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"R5QCXZTQGMQCTR5R","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"R5QCXZTQ","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:a74ba282660c5dc718a7e5468d5f69960fda4977e86074f2f634a628dffaa339","target":"graph","created_at":"2026-05-18T01:26:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Bloch-Okounkov studied certain functions on partitions $f$ called shifted symmetric polynomials. They showed that certain $q$-series arising from these functions (the so-called \\emph{$q$-brackets} $\\left<f\\right>_q$) are quasimodular forms. 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 $\\left<Q_k\\right>_q$.","authors_text":"Marie Jameson, Michael Griffin, Sarah Trebat-Leder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-23T21:11:26Z","title":"On p-adic modular forms and the Bloch-Okounkov theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07161","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:07dcd746d314f06de327e04669b1bce32dab77de519e0a10321404386d90b5c1","target":"record","created_at":"2026-05-18T01:26:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"41d58535b7fb442c2999dfbfbe7421f23cac8b7ff8a4043a419d37310c99d046","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-23T21:11:26Z","title_canon_sha256":"b2cb1056e01800895b80d0cf2bf98d3d28b9f085cd07f627bcf476b121555b70"},"schema_version":"1.0","source":{"id":"1509.07161","kind":"arxiv","version":2}},"canonical_sha256":"8f602be670332029c7b17ec4df9195d8b0fc80cbd2c4c8624c4b93741e1bb854","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f602be670332029c7b17ec4df9195d8b0fc80cbd2c4c8624c4b93741e1bb854","first_computed_at":"2026-05-18T01:26:59.970903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:59.970903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qloY1iO0h5P7HSILhPTCllQkkTQStyGoxkhkobatliHr1FC5ODTSUsrfUpr8G2ICUoU0ikonRd0W0Sa4flu6Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:59.971568Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.07161","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07dcd746d314f06de327e04669b1bce32dab77de519e0a10321404386d90b5c1","sha256:a74ba282660c5dc718a7e5468d5f69960fda4977e86074f2f634a628dffaa339"],"state_sha256":"7f3002ba8e55392218905c4254ff8e7c229c54ba51428716c7e25b8acd877668"}