{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:T6C3AX42QADSCJMQBEY4N3LRHG","short_pith_number":"pith:T6C3AX42","schema_version":"1.0","canonical_sha256":"9f85b05f9a80072125900931c6ed71398891e5de91916bf6fe34b70b8b3daf55","source":{"kind":"arxiv","id":"1803.10273","version":2},"attestation_state":"computed","paper":{"title":"Non-cuspidal Hida theory for Siegel modular forms and trivial zeros of $p$-adic $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Giovanni Rosso, Zheng Liu","submitted_at":"2018-03-27T18:59:39Z","abstract_excerpt":"We study the derivative of the standard $p$-adic $L$-function associated with a $P$-ordinary Siegel modular form (for $P$ a parabolic subgroup of $\\mathrm{GL}(n)$) when it presents a semi-stable trivial zero. This implies part of Greenberg's conjecture on the order and leading coefficient of $p$-adic $L$-functions at such trivial zero. We use the method of Greenberg-Stevens. For the construction of the improved $p$-adic $L$-function we develop Hida theory for non-cuspidal Siegel modular forms."},"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":"1803.10273","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-27T18:59:39Z","cross_cats_sorted":[],"title_canon_sha256":"01b8ca2aa7d4e8b1e071af97b0176db055175261d7bbf826b8085d52d79946f3","abstract_canon_sha256":"39b1907ed7b30dfb3b712667ce2bd7ea151d850e7413208531affcdff1b30913"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:18:52.518282Z","signature_b64":"AnbwRmUQIRNohW7ePRCtY5JQR1jq6ZoyjpFO6AQVjOejWmr6iZZdX3XT6IyDsNOX8O/qhjnTxC/ErzhOXW5dBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f85b05f9a80072125900931c6ed71398891e5de91916bf6fe34b70b8b3daf55","last_reissued_at":"2026-07-05T07:18:52.517800Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:18:52.517800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-cuspidal Hida theory for Siegel modular forms and trivial zeros of $p$-adic $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Giovanni Rosso, Zheng Liu","submitted_at":"2018-03-27T18:59:39Z","abstract_excerpt":"We study the derivative of the standard $p$-adic $L$-function associated with a $P$-ordinary Siegel modular form (for $P$ a parabolic subgroup of $\\mathrm{GL}(n)$) when it presents a semi-stable trivial zero. This implies part of Greenberg's conjecture on the order and leading coefficient of $p$-adic $L$-functions at such trivial zero. We use the method of Greenberg-Stevens. For the construction of the improved $p$-adic $L$-function we develop Hida theory for non-cuspidal Siegel modular forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10273","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1803.10273/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":"1803.10273","created_at":"2026-07-05T07:18:52.517857+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.10273v2","created_at":"2026-07-05T07:18:52.517857+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10273","created_at":"2026-07-05T07:18:52.517857+00:00"},{"alias_kind":"pith_short_12","alias_value":"T6C3AX42QADS","created_at":"2026-07-05T07:18:52.517857+00:00"},{"alias_kind":"pith_short_16","alias_value":"T6C3AX42QADSCJMQ","created_at":"2026-07-05T07:18:52.517857+00:00"},{"alias_kind":"pith_short_8","alias_value":"T6C3AX42","created_at":"2026-07-05T07:18:52.517857+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.07205","citing_title":"Iwasawa theory for $\\mathrm{U}(r,s)$, Bloch-Kato conjecture and Functional Equation","ref_index":22,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/T6C3AX42QADSCJMQBEY4N3LRHG","json":"https://pith.science/pith/T6C3AX42QADSCJMQBEY4N3LRHG.json","graph_json":"https://pith.science/api/pith-number/T6C3AX42QADSCJMQBEY4N3LRHG/graph.json","events_json":"https://pith.science/api/pith-number/T6C3AX42QADSCJMQBEY4N3LRHG/events.json","paper":"https://pith.science/paper/T6C3AX42"},"agent_actions":{"view_html":"https://pith.science/pith/T6C3AX42QADSCJMQBEY4N3LRHG","download_json":"https://pith.science/pith/T6C3AX42QADSCJMQBEY4N3LRHG.json","view_paper":"https://pith.science/paper/T6C3AX42","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.10273&json=true","fetch_graph":"https://pith.science/api/pith-number/T6C3AX42QADSCJMQBEY4N3LRHG/graph.json","fetch_events":"https://pith.science/api/pith-number/T6C3AX42QADSCJMQBEY4N3LRHG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T6C3AX42QADSCJMQBEY4N3LRHG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T6C3AX42QADSCJMQBEY4N3LRHG/action/storage_attestation","attest_author":"https://pith.science/pith/T6C3AX42QADSCJMQBEY4N3LRHG/action/author_attestation","sign_citation":"https://pith.science/pith/T6C3AX42QADSCJMQBEY4N3LRHG/action/citation_signature","submit_replication":"https://pith.science/pith/T6C3AX42QADSCJMQBEY4N3LRHG/action/replication_record"}},"created_at":"2026-07-05T07:18:52.517857+00:00","updated_at":"2026-07-05T07:18:52.517857+00:00"}