{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:OD45XPOGUVEWLOLUOHF3WJSLF5","short_pith_number":"pith:OD45XPOG","schema_version":"1.0","canonical_sha256":"70f9dbbdc6a54965b97471cbbb264b2f6b4fe79e8c3bda5a823f86365ea11909","source":{"kind":"arxiv","id":"1706.05167","version":4},"attestation_state":"computed","paper":{"title":"Rankin-Selberg periods for spherical principal series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Feng Su, Jan Frahm","submitted_at":"2017-06-16T07:49:37Z","abstract_excerpt":"By the unfolding method, Rankin-Selberg L-functions for ${\\rm GL}(n)\\times{\\rm GL}(m)$ can be expressed in terms of period integrals. These period integrals actually define invariant forms on tensor products of the relevant automorphic representations. By the multiplicity-one theorems due to Sun-Zhu and Chen-Sun such invariant forms are unique up to scalar multiples and can therefore be related to invariant forms on equivalent principal series representations. We construct meromorphic families of such invariant forms for spherical principal series representations of ${\\rm GL}(n,\\mathbb{R})$ an"},"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":"1706.05167","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-16T07:49:37Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"5c3a6982afc1c4e12e1d4acd76923186503ce4652ab37655419230a3adae1187","abstract_canon_sha256":"4ea9290e033dc07b94a3eea2229a039e12bd19afad490c43ecd936c79de17e1c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:03:31.898950Z","signature_b64":"TpfHjyTtaihQMxgvOFyfUk+xnCjPhqQ73398xYFJmI/sxYQMFbd1//eDkMI8+44rQir+to/LCXmhzpdUFHn+CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70f9dbbdc6a54965b97471cbbb264b2f6b4fe79e8c3bda5a823f86365ea11909","last_reissued_at":"2026-07-05T05:03:31.898429Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:03:31.898429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rankin-Selberg periods for spherical principal series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Feng Su, Jan Frahm","submitted_at":"2017-06-16T07:49:37Z","abstract_excerpt":"By the unfolding method, Rankin-Selberg L-functions for ${\\rm GL}(n)\\times{\\rm GL}(m)$ can be expressed in terms of period integrals. These period integrals actually define invariant forms on tensor products of the relevant automorphic representations. By the multiplicity-one theorems due to Sun-Zhu and Chen-Sun such invariant forms are unique up to scalar multiples and can therefore be related to invariant forms on equivalent principal series representations. We construct meromorphic families of such invariant forms for spherical principal series representations of ${\\rm GL}(n,\\mathbb{R})$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05167","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1706.05167/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1706.05167","created_at":"2026-07-05T05:03:31.898558+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.05167v4","created_at":"2026-07-05T05:03:31.898558+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.05167","created_at":"2026-07-05T05:03:31.898558+00:00"},{"alias_kind":"pith_short_12","alias_value":"OD45XPOGUVEW","created_at":"2026-07-05T05:03:31.898558+00:00"},{"alias_kind":"pith_short_16","alias_value":"OD45XPOGUVEWLOLU","created_at":"2026-07-05T05:03:31.898558+00:00"},{"alias_kind":"pith_short_8","alias_value":"OD45XPOG","created_at":"2026-07-05T05:03:31.898558+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/OD45XPOGUVEWLOLUOHF3WJSLF5","json":"https://pith.science/pith/OD45XPOGUVEWLOLUOHF3WJSLF5.json","graph_json":"https://pith.science/api/pith-number/OD45XPOGUVEWLOLUOHF3WJSLF5/graph.json","events_json":"https://pith.science/api/pith-number/OD45XPOGUVEWLOLUOHF3WJSLF5/events.json","paper":"https://pith.science/paper/OD45XPOG"},"agent_actions":{"view_html":"https://pith.science/pith/OD45XPOGUVEWLOLUOHF3WJSLF5","download_json":"https://pith.science/pith/OD45XPOGUVEWLOLUOHF3WJSLF5.json","view_paper":"https://pith.science/paper/OD45XPOG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.05167&json=true","fetch_graph":"https://pith.science/api/pith-number/OD45XPOGUVEWLOLUOHF3WJSLF5/graph.json","fetch_events":"https://pith.science/api/pith-number/OD45XPOGUVEWLOLUOHF3WJSLF5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OD45XPOGUVEWLOLUOHF3WJSLF5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OD45XPOGUVEWLOLUOHF3WJSLF5/action/storage_attestation","attest_author":"https://pith.science/pith/OD45XPOGUVEWLOLUOHF3WJSLF5/action/author_attestation","sign_citation":"https://pith.science/pith/OD45XPOGUVEWLOLUOHF3WJSLF5/action/citation_signature","submit_replication":"https://pith.science/pith/OD45XPOGUVEWLOLUOHF3WJSLF5/action/replication_record"}},"created_at":"2026-07-05T05:03:31.898558+00:00","updated_at":"2026-07-05T05:03:31.898558+00:00"}