{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YFVNS57WOAQ2SD2KL7SYILTSRD","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":"b822abca6b64e772215e72828c6f58089aa047f417b5540b2d336c72cf8e7d1f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-13T21:33:56Z","title_canon_sha256":"c947a42145123515f7c4da6f0513730c0a48be2979447660c8ac39c79944f29d"},"schema_version":"1.0","source":{"id":"1302.3249","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3249","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3249v3","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3249","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"pith_short_12","alias_value":"YFVNS57WOAQ2","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YFVNS57WOAQ2SD2K","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YFVNS57W","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:da5f64be2c3981e8bd37901b4211425d78464bb774ac59b875ba62e5de5f67e6","target":"graph","created_at":"2026-05-18T01:04:04Z","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":"The purpose of this article is to generalize some results of Vatsal on studying the special values of Rankin-Selberg L-functions in an anticyclotomic $\\mathbb{Z}_{p}$-extension. Let $g$ be a cuspidal Hilbert modular form of parallel weight (2,...,2) and level $\\mathcal{N}$ over a totally real field F, and let K/F be a totally imaginary quadratic extension of relative discriminant $\\mathcal{D}$. We study the $l$-adic valuation of the special values $L(g,\\chi,\\frac{1}{2})$ as \\chi varies over the ring class characters of K of $\\mathcal{P}$-power conductor, for some fixed prime ideal $\\mathcal{P}","authors_text":"Alia Hamieh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-13T21:33:56Z","title":"Special Values of Anticyclotomic L-functions Modulo \\lambda"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3249","kind":"arxiv","version":3},"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:aca8ae3cbe498d7eb83dcbefa5e6b61750131b46125d00dcbef2b03d1aa18991","target":"record","created_at":"2026-05-18T01:04:04Z","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":"b822abca6b64e772215e72828c6f58089aa047f417b5540b2d336c72cf8e7d1f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-13T21:33:56Z","title_canon_sha256":"c947a42145123515f7c4da6f0513730c0a48be2979447660c8ac39c79944f29d"},"schema_version":"1.0","source":{"id":"1302.3249","kind":"arxiv","version":3}},"canonical_sha256":"c16ad977f67021a90f4a5fe5842e7288e94e26c982ec55ed06ddc01eaed16a62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c16ad977f67021a90f4a5fe5842e7288e94e26c982ec55ed06ddc01eaed16a62","first_computed_at":"2026-05-18T01:04:04.387852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:04.387852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lAV6IcpC5AiYTqcHgDvlVZJ8qAwjMMnw+ZsEaKQj+PWGtzR0aZ9GvYhBCuPYr9ZdSXyuM03Cr7sCALkpBMJrCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:04.388287Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3249","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aca8ae3cbe498d7eb83dcbefa5e6b61750131b46125d00dcbef2b03d1aa18991","sha256:da5f64be2c3981e8bd37901b4211425d78464bb774ac59b875ba62e5de5f67e6"],"state_sha256":"53e3ff3109436cbbd8209ff7ad2a2b63396010e3d76627cf7a2197252c10cd76"}