{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:WEUWC7NODQ7VDY2AUGJINX27HK","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":"1aeeb3a1611245b782db00c4aff7396a5c4bac6f6d7c91878d44c76c68523c2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-01-12T20:08:13Z","title_canon_sha256":"347f768ce10236e9665bb55c94c5eeadcd3884208bd9a5357df04951e9c26847"},"schema_version":"1.0","source":{"id":"1001.1913","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.1913","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"arxiv_version","alias_value":"1001.1913v5","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.1913","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"pith_short_12","alias_value":"WEUWC7NODQ7V","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"WEUWC7NODQ7VDY2A","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"WEUWC7NO","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:80a1baefb2b2ee30a6566d3949af12d1979fedc20423363d57eb6d186fa4b7ac","target":"graph","created_at":"2026-05-18T03:38:12Z","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":"We introduce an analog of part of the Langlands-Shahidi method to the p-adic setting, constructing reciprocals of certain p-adic L-functions using the nonconstant terms of the Fourier expansions of Eisenstein series. We carry out the method for the group SL(2), and give explicit p-adic measures whose Mellin transforms are reciprocals of Dirichlet L-functions.","authors_text":"Alexei Pantchichkine, Freydoon Shahidi, Stephen D. Miller, Stephen Gelbart","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-01-12T20:08:13Z","title":"A p-adic integral for the reciprocal of L-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1913","kind":"arxiv","version":5},"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":"sha256:721688beafc6707c839f04916aa89ffd7e99e3dc8abf5c11258b987ec782db40","target":"record","created_at":"2026-05-18T03:38:12Z","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":"1aeeb3a1611245b782db00c4aff7396a5c4bac6f6d7c91878d44c76c68523c2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-01-12T20:08:13Z","title_canon_sha256":"347f768ce10236e9665bb55c94c5eeadcd3884208bd9a5357df04951e9c26847"},"schema_version":"1.0","source":{"id":"1001.1913","kind":"arxiv","version":5}},"canonical_sha256":"b129617dae1c3f51e340a19286df5f3aa7ae8446935346be6518db887d867dbd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b129617dae1c3f51e340a19286df5f3aa7ae8446935346be6518db887d867dbd","first_computed_at":"2026-05-18T03:38:12.833597Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:12.833597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4WWzZXrDnCNu1VNlQNLRkJbM0BuPGTUbxqPPqPt21K/lvMt3rKWna5SkOI57Wz/6oTQdN+eNG0gB4a1NV/73DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:12.834234Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.1913","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:721688beafc6707c839f04916aa89ffd7e99e3dc8abf5c11258b987ec782db40","sha256:80a1baefb2b2ee30a6566d3949af12d1979fedc20423363d57eb6d186fa4b7ac"],"state_sha256":"5b2efda9863423787116e5d4456aa28aab10269aea99223077099a1215f97f36"}