{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:YBU6I6ICQDGEFFNEJJTPPLWO3E","short_pith_number":"pith:YBU6I6IC","schema_version":"1.0","canonical_sha256":"c069e4790280cc4295a44a66f7aeced91e3c35701a6ae696e099cd601aea6e7b","source":{"kind":"arxiv","id":"1005.5135","version":2},"attestation_state":"computed","paper":{"title":"Shimura correspondence for level $p^2$ and the central values of $L$-series II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ariel Pacetti, Gonzalo Tornar\\'ia","submitted_at":"2010-05-27T18:01:29Z","abstract_excerpt":"Given a Hecke eigenform $f$ of weight $2$ and square-free level $N$, by the work of Kohnen, there is a unique weight $3/2$ modular form of level $4N$ mapping to $f$ under the Shimura correspondence. Furthermore, by the work of Waldspurger the Fourier coefficients of such a form are related to the quadratic twists of the form $f$. Gross gave a construction of the half integral weight form when $N$ is prime, and such construction was later generalized to square-free levels. However, in the non-square free case, the situation is more complicated since the natural construction is vacuous. The prob"},"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":"1005.5135","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-27T18:01:29Z","cross_cats_sorted":[],"title_canon_sha256":"01148c0a75680555da7e626e3abe4d1adbe962b12b8d812bfef50b047b9654c9","abstract_canon_sha256":"c26ffec324953d060126dc0c6f2b78fcfaf392ac825712690924fee6b0692352"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:18.894877Z","signature_b64":"q0jDpeyV2DuE6sutGQ5DZeyDdF8KHRqtaYNd+xqcv6RYvlL0spVdtkb9lTAwGkCUbQCBzsIFpXI5R5hxAsgyCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c069e4790280cc4295a44a66f7aeced91e3c35701a6ae696e099cd601aea6e7b","last_reissued_at":"2026-05-18T02:55:18.894327Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:18.894327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shimura correspondence for level $p^2$ and the central values of $L$-series II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ariel Pacetti, Gonzalo Tornar\\'ia","submitted_at":"2010-05-27T18:01:29Z","abstract_excerpt":"Given a Hecke eigenform $f$ of weight $2$ and square-free level $N$, by the work of Kohnen, there is a unique weight $3/2$ modular form of level $4N$ mapping to $f$ under the Shimura correspondence. Furthermore, by the work of Waldspurger the Fourier coefficients of such a form are related to the quadratic twists of the form $f$. Gross gave a construction of the half integral weight form when $N$ is prime, and such construction was later generalized to square-free levels. However, in the non-square free case, the situation is more complicated since the natural construction is vacuous. The prob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.5135","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1005.5135","created_at":"2026-05-18T02:55:18.894402+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.5135v2","created_at":"2026-05-18T02:55:18.894402+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.5135","created_at":"2026-05-18T02:55:18.894402+00:00"},{"alias_kind":"pith_short_12","alias_value":"YBU6I6ICQDGE","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"YBU6I6ICQDGEFFNE","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"YBU6I6IC","created_at":"2026-05-18T12:26:17.028572+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/YBU6I6ICQDGEFFNEJJTPPLWO3E","json":"https://pith.science/pith/YBU6I6ICQDGEFFNEJJTPPLWO3E.json","graph_json":"https://pith.science/api/pith-number/YBU6I6ICQDGEFFNEJJTPPLWO3E/graph.json","events_json":"https://pith.science/api/pith-number/YBU6I6ICQDGEFFNEJJTPPLWO3E/events.json","paper":"https://pith.science/paper/YBU6I6IC"},"agent_actions":{"view_html":"https://pith.science/pith/YBU6I6ICQDGEFFNEJJTPPLWO3E","download_json":"https://pith.science/pith/YBU6I6ICQDGEFFNEJJTPPLWO3E.json","view_paper":"https://pith.science/paper/YBU6I6IC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.5135&json=true","fetch_graph":"https://pith.science/api/pith-number/YBU6I6ICQDGEFFNEJJTPPLWO3E/graph.json","fetch_events":"https://pith.science/api/pith-number/YBU6I6ICQDGEFFNEJJTPPLWO3E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YBU6I6ICQDGEFFNEJJTPPLWO3E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YBU6I6ICQDGEFFNEJJTPPLWO3E/action/storage_attestation","attest_author":"https://pith.science/pith/YBU6I6ICQDGEFFNEJJTPPLWO3E/action/author_attestation","sign_citation":"https://pith.science/pith/YBU6I6ICQDGEFFNEJJTPPLWO3E/action/citation_signature","submit_replication":"https://pith.science/pith/YBU6I6ICQDGEFFNEJJTPPLWO3E/action/replication_record"}},"created_at":"2026-05-18T02:55:18.894402+00:00","updated_at":"2026-05-18T02:55:18.894402+00:00"}