{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7Q4FAUWJRDNLXWU7ZGLAWMAHF3","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":"f054dc0aa551be2331d8a6e5f52b7f23f3eff6f214ddaa0ff57d50d132ffa39b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-10T10:16:35Z","title_canon_sha256":"b92f2e779fe582822e2f897d0265b99001718d7f0867c18de2614991c19c5241"},"schema_version":"1.0","source":{"id":"1207.2289","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2289","created_at":"2026-05-18T03:36:15Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2289v2","created_at":"2026-05-18T03:36:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2289","created_at":"2026-05-18T03:36:15Z"},{"alias_kind":"pith_short_12","alias_value":"7Q4FAUWJRDNL","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7Q4FAUWJRDNLXWU7","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7Q4FAUWJ","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:0de6063e3c7f05312ae7c42a0c9b73229ad2cb391b5dc0f30d8e2a41cfb49b63","target":"graph","created_at":"2026-05-18T03:36:15Z","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":"Let $E$ be a modular elliptic curve over a totally real number field $F$. We prove the weak exceptional zero conjecture which links a (higher) derivative of the $p$-adic $L$-function attached to $E$ to certain $p$-adic periods attached to the corresponding Hilbert modular form at the places above $p$ where $E$ has split multiplicative reduction. Under some mild restrictions on $p$ and the conductor of $E$ we deduce the exceptional zero conjecture in the strong form (i.e.\\ where the automorphic $p$-adic periods are replaced by the $\\cL$-invariants of $E$ defined in terms of Tate periods) from a","authors_text":"Michael Spiess","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-10T10:16:35Z","title":"On special zeros of $p$-adic $L$-functions of Hilbert modular forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2289","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:d25d3db4e6880f512ed938d2c01bca2d8c29ae4aec41fa5ef020d2e6d9a01c1f","target":"record","created_at":"2026-05-18T03:36:15Z","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":"f054dc0aa551be2331d8a6e5f52b7f23f3eff6f214ddaa0ff57d50d132ffa39b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-10T10:16:35Z","title_canon_sha256":"b92f2e779fe582822e2f897d0265b99001718d7f0867c18de2614991c19c5241"},"schema_version":"1.0","source":{"id":"1207.2289","kind":"arxiv","version":2}},"canonical_sha256":"fc385052c988dabbda9fc9960b30072ecda78930d9e9cf246faa6494be146879","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc385052c988dabbda9fc9960b30072ecda78930d9e9cf246faa6494be146879","first_computed_at":"2026-05-18T03:36:15.957133Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:15.957133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FkOzbR4xEtcO5xVmQmDxlWnQN5CQv7f4d18td5sbtZqZx4ymVtlkaOCJB3guZLoUledTpdgI+4ljc7MVuz/7Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:15.957685Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.2289","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d25d3db4e6880f512ed938d2c01bca2d8c29ae4aec41fa5ef020d2e6d9a01c1f","sha256:0de6063e3c7f05312ae7c42a0c9b73229ad2cb391b5dc0f30d8e2a41cfb49b63"],"state_sha256":"9101e9ec827a3eff33529eaaae685d768760e4ed4ae0f75a09c274641a3ac2f0"}