{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:PMOS2C2O5DWKGIOAQXKOGFXA62","short_pith_number":"pith:PMOS2C2O","schema_version":"1.0","canonical_sha256":"7b1d2d0b4ee8eca321c085d4e316e0f69f4a618314bbf945f8678e9aafb11aa1","source":{"kind":"arxiv","id":"1702.05004","version":2},"attestation_state":"computed","paper":{"title":"Integral representation and critical $L$-values for holomorphic forms on $GSp_{2n} \\times GL_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Abhishek Saha, Ameya Pitale, Ralf Schmidt","submitted_at":"2017-02-16T15:04:17Z","abstract_excerpt":"We prove an explicit integral representation -- involving the pullback of a suitable Siegel Eisenstein series -- for the twisted standard $L$-function associated to a holomorphic vector-valued Siegel cusp form of degree $n$ and arbitrary level. In contrast to all previously proved pullback formulas in this situation, our formula involves only scalar-valued functions despite being applicable to $L$-functions of vector-valued Siegel cusp forms. The key new ingredient in our method is a novel choice of local vectors at the archimedean place which allows us to exactly compute the archimedean local"},"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":"1702.05004","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-16T15:04:17Z","cross_cats_sorted":[],"title_canon_sha256":"5eef15c669d57daf9c39ad9d637ca3c5e0f9d49c250b979a8f318240055ad8db","abstract_canon_sha256":"cb256822c3da41fa88cf0fa49303efb2a9ad8269b764129fa029ab3ff44f29b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:27.646166Z","signature_b64":"ro7d/E3eUTqqQszT3ELcxySbXlpil+PlSlDx3zhoSIDao31+A7lsmpzjdtK1hZa1bsnjuI5W8QkFzmnHKyocBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b1d2d0b4ee8eca321c085d4e316e0f69f4a618314bbf945f8678e9aafb11aa1","last_reissued_at":"2026-05-18T00:20:27.645431Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:27.645431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integral representation and critical $L$-values for holomorphic forms on $GSp_{2n} \\times GL_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Abhishek Saha, Ameya Pitale, Ralf Schmidt","submitted_at":"2017-02-16T15:04:17Z","abstract_excerpt":"We prove an explicit integral representation -- involving the pullback of a suitable Siegel Eisenstein series -- for the twisted standard $L$-function associated to a holomorphic vector-valued Siegel cusp form of degree $n$ and arbitrary level. In contrast to all previously proved pullback formulas in this situation, our formula involves only scalar-valued functions despite being applicable to $L$-functions of vector-valued Siegel cusp forms. The key new ingredient in our method is a novel choice of local vectors at the archimedean place which allows us to exactly compute the archimedean local"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05004","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":"1702.05004","created_at":"2026-05-18T00:20:27.645540+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.05004v2","created_at":"2026-05-18T00:20:27.645540+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05004","created_at":"2026-05-18T00:20:27.645540+00:00"},{"alias_kind":"pith_short_12","alias_value":"PMOS2C2O5DWK","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"PMOS2C2O5DWKGIOA","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"PMOS2C2O","created_at":"2026-05-18T12:31:37.085036+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/PMOS2C2O5DWKGIOAQXKOGFXA62","json":"https://pith.science/pith/PMOS2C2O5DWKGIOAQXKOGFXA62.json","graph_json":"https://pith.science/api/pith-number/PMOS2C2O5DWKGIOAQXKOGFXA62/graph.json","events_json":"https://pith.science/api/pith-number/PMOS2C2O5DWKGIOAQXKOGFXA62/events.json","paper":"https://pith.science/paper/PMOS2C2O"},"agent_actions":{"view_html":"https://pith.science/pith/PMOS2C2O5DWKGIOAQXKOGFXA62","download_json":"https://pith.science/pith/PMOS2C2O5DWKGIOAQXKOGFXA62.json","view_paper":"https://pith.science/paper/PMOS2C2O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.05004&json=true","fetch_graph":"https://pith.science/api/pith-number/PMOS2C2O5DWKGIOAQXKOGFXA62/graph.json","fetch_events":"https://pith.science/api/pith-number/PMOS2C2O5DWKGIOAQXKOGFXA62/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PMOS2C2O5DWKGIOAQXKOGFXA62/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PMOS2C2O5DWKGIOAQXKOGFXA62/action/storage_attestation","attest_author":"https://pith.science/pith/PMOS2C2O5DWKGIOAQXKOGFXA62/action/author_attestation","sign_citation":"https://pith.science/pith/PMOS2C2O5DWKGIOAQXKOGFXA62/action/citation_signature","submit_replication":"https://pith.science/pith/PMOS2C2O5DWKGIOAQXKOGFXA62/action/replication_record"}},"created_at":"2026-05-18T00:20:27.645540+00:00","updated_at":"2026-05-18T00:20:27.645540+00:00"}