{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:GPGTCNJTLOSQMB6G7DWCO7HM6Y","short_pith_number":"pith:GPGTCNJT","schema_version":"1.0","canonical_sha256":"33cd3135335ba50607c6f8ec277cecf6145eb868842db4ad7217063d55e677df","source":{"kind":"arxiv","id":"1903.03458","version":1},"attestation_state":"computed","paper":{"title":"Test vectors for Rankin-Selberg $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Andrew R. Booker, Min Lee, M. Krishnamurthy","submitted_at":"2019-03-08T16:07:14Z","abstract_excerpt":"We study the local zeta integrals attached to a pair of generic representations $(\\pi,\\tau)$ of $GL_n\\times GL_m$, $n>m$, over a $p$-adic field. Through a process of unipotent averaging we produce a pair of corresponding Whittaker functions whose zeta integral is non-zero, and we express this integral in terms of the Langlands parameters of $\\pi$ and $\\tau$. In many cases, these Whittaker functions also serve as a test vector for the associated Rankin-Selberg (local) $L$-function."},"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":"1903.03458","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-08T16:07:14Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"1a54672e2ed33e4e0c67fe12fefd82d1734df2cc45dca88ad95faaeba4f6025f","abstract_canon_sha256":"6cbddcae3f8fce969fa7b24905085cd54d749884a7d5fd95edbc79512e74760c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:45.439781Z","signature_b64":"f1k152ftsshD/59VpQ+fC2kCGnz92Br9c0C9qeTxUAlnrlNH3uyQ1TXghb5uJPJHYQRu/soO8xKFRWlZBHcsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33cd3135335ba50607c6f8ec277cecf6145eb868842db4ad7217063d55e677df","last_reissued_at":"2026-05-17T23:51:45.438959Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:45.438959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Test vectors for Rankin-Selberg $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Andrew R. Booker, Min Lee, M. Krishnamurthy","submitted_at":"2019-03-08T16:07:14Z","abstract_excerpt":"We study the local zeta integrals attached to a pair of generic representations $(\\pi,\\tau)$ of $GL_n\\times GL_m$, $n>m$, over a $p$-adic field. Through a process of unipotent averaging we produce a pair of corresponding Whittaker functions whose zeta integral is non-zero, and we express this integral in terms of the Langlands parameters of $\\pi$ and $\\tau$. In many cases, these Whittaker functions also serve as a test vector for the associated Rankin-Selberg (local) $L$-function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03458","kind":"arxiv","version":1},"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":"1903.03458","created_at":"2026-05-17T23:51:45.439073+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.03458v1","created_at":"2026-05-17T23:51:45.439073+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.03458","created_at":"2026-05-17T23:51:45.439073+00:00"},{"alias_kind":"pith_short_12","alias_value":"GPGTCNJTLOSQ","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"GPGTCNJTLOSQMB6G","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"GPGTCNJT","created_at":"2026-05-18T12:33:18.533446+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/GPGTCNJTLOSQMB6G7DWCO7HM6Y","json":"https://pith.science/pith/GPGTCNJTLOSQMB6G7DWCO7HM6Y.json","graph_json":"https://pith.science/api/pith-number/GPGTCNJTLOSQMB6G7DWCO7HM6Y/graph.json","events_json":"https://pith.science/api/pith-number/GPGTCNJTLOSQMB6G7DWCO7HM6Y/events.json","paper":"https://pith.science/paper/GPGTCNJT"},"agent_actions":{"view_html":"https://pith.science/pith/GPGTCNJTLOSQMB6G7DWCO7HM6Y","download_json":"https://pith.science/pith/GPGTCNJTLOSQMB6G7DWCO7HM6Y.json","view_paper":"https://pith.science/paper/GPGTCNJT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.03458&json=true","fetch_graph":"https://pith.science/api/pith-number/GPGTCNJTLOSQMB6G7DWCO7HM6Y/graph.json","fetch_events":"https://pith.science/api/pith-number/GPGTCNJTLOSQMB6G7DWCO7HM6Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GPGTCNJTLOSQMB6G7DWCO7HM6Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GPGTCNJTLOSQMB6G7DWCO7HM6Y/action/storage_attestation","attest_author":"https://pith.science/pith/GPGTCNJTLOSQMB6G7DWCO7HM6Y/action/author_attestation","sign_citation":"https://pith.science/pith/GPGTCNJTLOSQMB6G7DWCO7HM6Y/action/citation_signature","submit_replication":"https://pith.science/pith/GPGTCNJTLOSQMB6G7DWCO7HM6Y/action/replication_record"}},"created_at":"2026-05-17T23:51:45.439073+00:00","updated_at":"2026-05-17T23:51:45.439073+00:00"}