{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ZKW55KQ7CSLLMLWNGKJDXH7QT7","short_pith_number":"pith:ZKW55KQ7","schema_version":"1.0","canonical_sha256":"caaddeaa1f1496b62ecd32923b9ff09fda60ac903f4a47b02fafc635d7b920c5","source":{"kind":"arxiv","id":"1401.1431","version":2},"attestation_state":"computed","paper":{"title":"Derivative of symmetric square p-adic L-functions via pull-back formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Giovanni Rosso","submitted_at":"2014-01-07T16:22:13Z","abstract_excerpt":"In this paper we recall the method of Greenberg and Stevens to calculate derivatives of p-adic L-functions using deformations of Galois representation and we apply it to the symmetric square of a modular form Steinberg at p. Under certain hypotheses on the conductor and the Nebentypus, this prove a conjecture of Greenberg and Benois on trivial zeros."},"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":"1401.1431","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-07T16:22:13Z","cross_cats_sorted":[],"title_canon_sha256":"bc53f9db7355ed1f793ec5ad8b767f67de13b4280710dd400f434eab6dbe2165","abstract_canon_sha256":"19ca499e199a48bbb1ced16748692c1e363b2e2051850000378ae453fe2ea46a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:24.212772Z","signature_b64":"45lr2cR7owlqWB/rc+V+z3zX2gYPybphzx0g0D68xr3yVlr5PMK9w4B3JXgV3Rh3tystphWu5lCPpDRFv+ftDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"caaddeaa1f1496b62ecd32923b9ff09fda60ac903f4a47b02fafc635d7b920c5","last_reissued_at":"2026-05-18T00:16:24.211976Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:24.211976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Derivative of symmetric square p-adic L-functions via pull-back formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Giovanni Rosso","submitted_at":"2014-01-07T16:22:13Z","abstract_excerpt":"In this paper we recall the method of Greenberg and Stevens to calculate derivatives of p-adic L-functions using deformations of Galois representation and we apply it to the symmetric square of a modular form Steinberg at p. Under certain hypotheses on the conductor and the Nebentypus, this prove a conjecture of Greenberg and Benois on trivial zeros."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1431","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":"1401.1431","created_at":"2026-05-18T00:16:24.212053+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.1431v2","created_at":"2026-05-18T00:16:24.212053+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1431","created_at":"2026-05-18T00:16:24.212053+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZKW55KQ7CSLL","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZKW55KQ7CSLLMLWN","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZKW55KQ7","created_at":"2026-05-18T12:28:59.999130+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/ZKW55KQ7CSLLMLWNGKJDXH7QT7","json":"https://pith.science/pith/ZKW55KQ7CSLLMLWNGKJDXH7QT7.json","graph_json":"https://pith.science/api/pith-number/ZKW55KQ7CSLLMLWNGKJDXH7QT7/graph.json","events_json":"https://pith.science/api/pith-number/ZKW55KQ7CSLLMLWNGKJDXH7QT7/events.json","paper":"https://pith.science/paper/ZKW55KQ7"},"agent_actions":{"view_html":"https://pith.science/pith/ZKW55KQ7CSLLMLWNGKJDXH7QT7","download_json":"https://pith.science/pith/ZKW55KQ7CSLLMLWNGKJDXH7QT7.json","view_paper":"https://pith.science/paper/ZKW55KQ7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.1431&json=true","fetch_graph":"https://pith.science/api/pith-number/ZKW55KQ7CSLLMLWNGKJDXH7QT7/graph.json","fetch_events":"https://pith.science/api/pith-number/ZKW55KQ7CSLLMLWNGKJDXH7QT7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZKW55KQ7CSLLMLWNGKJDXH7QT7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZKW55KQ7CSLLMLWNGKJDXH7QT7/action/storage_attestation","attest_author":"https://pith.science/pith/ZKW55KQ7CSLLMLWNGKJDXH7QT7/action/author_attestation","sign_citation":"https://pith.science/pith/ZKW55KQ7CSLLMLWNGKJDXH7QT7/action/citation_signature","submit_replication":"https://pith.science/pith/ZKW55KQ7CSLLMLWNGKJDXH7QT7/action/replication_record"}},"created_at":"2026-05-18T00:16:24.212053+00:00","updated_at":"2026-05-18T00:16:24.212053+00:00"}