{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:IYYLE2HN2INIDGN2JU5GJQHFGM","short_pith_number":"pith:IYYLE2HN","schema_version":"1.0","canonical_sha256":"4630b268edd21a8199ba4d3a64c0e53335fce41f3805df8d6af5f9b699b6be20","source":{"kind":"arxiv","id":"2009.04955","version":3},"attestation_state":"computed","paper":{"title":"Polar harmonic Maa{\\ss} forms and holomorphic projection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andreas Mono, Joshua Males, Larry Rolen","submitted_at":"2020-09-10T15:51:56Z","abstract_excerpt":"Recently, Mertens, Ono, and the third author studied mock modular analogues of Eisenstein series. Their coefficients are given by small divisor functions, and have shadows given by classical Shimura theta functions. Here, we construct a class of small divisor functions $\\sigma^{\\text{sm}}_{2,\\chi}$ and prove that these generate the holomorphic part of polar harmonic (weak) Maa{\\ss} forms of weight $\\frac{3}{2}$. To this end, we essentially compute the holomorphic projection of mixed harmonic Maa{\\ss} forms in terms of Jacobi polynomials, but without assuming the structure of such forms. Instea"},"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":"2009.04955","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-09-10T15:51:56Z","cross_cats_sorted":[],"title_canon_sha256":"f4ae57bcb1574b1405907190572e40c7071611ac65368dac5ada146c8a00acd4","abstract_canon_sha256":"0d632a4ce0383b09777469b5d8eece3dca7755fa98c9a018d4f058ccadd5f5ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:47:03.021294Z","signature_b64":"W2tUIE2e93yAeindTEX4GjzN58NiEWeVBhjuUIuAnovL27wcTo3J4ew5DUvT13OGrOVSBvya75IDBjsGqOYZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4630b268edd21a8199ba4d3a64c0e53335fce41f3805df8d6af5f9b699b6be20","last_reissued_at":"2026-07-05T08:47:03.020803Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:47:03.020803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polar harmonic Maa{\\ss} forms and holomorphic projection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andreas Mono, Joshua Males, Larry Rolen","submitted_at":"2020-09-10T15:51:56Z","abstract_excerpt":"Recently, Mertens, Ono, and the third author studied mock modular analogues of Eisenstein series. Their coefficients are given by small divisor functions, and have shadows given by classical Shimura theta functions. Here, we construct a class of small divisor functions $\\sigma^{\\text{sm}}_{2,\\chi}$ and prove that these generate the holomorphic part of polar harmonic (weak) Maa{\\ss} forms of weight $\\frac{3}{2}$. To this end, we essentially compute the holomorphic projection of mixed harmonic Maa{\\ss} forms in terms of Jacobi polynomials, but without assuming the structure of such forms. Instea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.04955","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2009.04955/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2009.04955","created_at":"2026-07-05T08:47:03.020859+00:00"},{"alias_kind":"arxiv_version","alias_value":"2009.04955v3","created_at":"2026-07-05T08:47:03.020859+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.04955","created_at":"2026-07-05T08:47:03.020859+00:00"},{"alias_kind":"pith_short_12","alias_value":"IYYLE2HN2INI","created_at":"2026-07-05T08:47:03.020859+00:00"},{"alias_kind":"pith_short_16","alias_value":"IYYLE2HN2INIDGN2","created_at":"2026-07-05T08:47:03.020859+00:00"},{"alias_kind":"pith_short_8","alias_value":"IYYLE2HN","created_at":"2026-07-05T08:47:03.020859+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IYYLE2HN2INIDGN2JU5GJQHFGM","json":"https://pith.science/pith/IYYLE2HN2INIDGN2JU5GJQHFGM.json","graph_json":"https://pith.science/api/pith-number/IYYLE2HN2INIDGN2JU5GJQHFGM/graph.json","events_json":"https://pith.science/api/pith-number/IYYLE2HN2INIDGN2JU5GJQHFGM/events.json","paper":"https://pith.science/paper/IYYLE2HN"},"agent_actions":{"view_html":"https://pith.science/pith/IYYLE2HN2INIDGN2JU5GJQHFGM","download_json":"https://pith.science/pith/IYYLE2HN2INIDGN2JU5GJQHFGM.json","view_paper":"https://pith.science/paper/IYYLE2HN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2009.04955&json=true","fetch_graph":"https://pith.science/api/pith-number/IYYLE2HN2INIDGN2JU5GJQHFGM/graph.json","fetch_events":"https://pith.science/api/pith-number/IYYLE2HN2INIDGN2JU5GJQHFGM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IYYLE2HN2INIDGN2JU5GJQHFGM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IYYLE2HN2INIDGN2JU5GJQHFGM/action/storage_attestation","attest_author":"https://pith.science/pith/IYYLE2HN2INIDGN2JU5GJQHFGM/action/author_attestation","sign_citation":"https://pith.science/pith/IYYLE2HN2INIDGN2JU5GJQHFGM/action/citation_signature","submit_replication":"https://pith.science/pith/IYYLE2HN2INIDGN2JU5GJQHFGM/action/replication_record"}},"created_at":"2026-07-05T08:47:03.020859+00:00","updated_at":"2026-07-05T08:47:03.020859+00:00"}