{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:RCTDGZQNHXPIBJHULHRZGE24AW","short_pith_number":"pith:RCTDGZQN","schema_version":"1.0","canonical_sha256":"88a633660d3dde80a4f459e393135c0595168c787fbff5f222b5dde96bb707cb","source":{"kind":"arxiv","id":"2411.12609","version":1},"attestation_state":"computed","paper":{"title":"Relative Trace Formula And Simultaneous Nonvanishing for GL_3 x GL_2 and GL_3 x GL_1 L-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dinakar Ramakrishnan, Liyang Yang, Philippe Michel","submitted_at":"2024-11-19T16:14:35Z","abstract_excerpt":"Fix a Dirichlet character $\\chi$ and a cuspidal GL$(2)$ eigenform $\\phi$ with relatively prime conductors. Then we show that there are infinitely many cusp forms $\\pi$ on GL$(3)$ such that $L(1/2, \\pi \\times \\chi)$ and $L(1/2, \\pi \\times \\phi)$ are simultaneously non-zero. We achieve this by use of Jacquet's Relative Trace Formula. We derive an expression of the average over the GL$(3)$ cuspidal spectrum as a sum of a non-zero main term and two subsidiary terms which are forced to be zero for large enough level by use of a suitable test function. This modest article is dedicated to the memory "},"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":"2411.12609","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-11-19T16:14:35Z","cross_cats_sorted":[],"title_canon_sha256":"b2c6afe4e48f331163c1c49b379fbf5796b83e8caa6d5392e288fed0a3f20257","abstract_canon_sha256":"1d449f4925cd1f6aa07ae5ba217966c503209fd465725030b2ade74055c6f31a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:37:45.546969Z","signature_b64":"C1R2Kff/pFItSJfvUarrcxNwaN0tXX43A5agSu4+KLCXG1QChf6C1GNJqbSmPkozKfkrIfVjEW9MnnJIyfdyAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88a633660d3dde80a4f459e393135c0595168c787fbff5f222b5dde96bb707cb","last_reissued_at":"2026-07-05T09:37:45.546517Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:37:45.546517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relative Trace Formula And Simultaneous Nonvanishing for GL_3 x GL_2 and GL_3 x GL_1 L-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dinakar Ramakrishnan, Liyang Yang, Philippe Michel","submitted_at":"2024-11-19T16:14:35Z","abstract_excerpt":"Fix a Dirichlet character $\\chi$ and a cuspidal GL$(2)$ eigenform $\\phi$ with relatively prime conductors. Then we show that there are infinitely many cusp forms $\\pi$ on GL$(3)$ such that $L(1/2, \\pi \\times \\chi)$ and $L(1/2, \\pi \\times \\phi)$ are simultaneously non-zero. We achieve this by use of Jacquet's Relative Trace Formula. We derive an expression of the average over the GL$(3)$ cuspidal spectrum as a sum of a non-zero main term and two subsidiary terms which are forced to be zero for large enough level by use of a suitable test function. This modest article is dedicated to the memory "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12609","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.12609/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":"2411.12609","created_at":"2026-07-05T09:37:45.546570+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.12609v1","created_at":"2026-07-05T09:37:45.546570+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.12609","created_at":"2026-07-05T09:37:45.546570+00:00"},{"alias_kind":"pith_short_12","alias_value":"RCTDGZQNHXPI","created_at":"2026-07-05T09:37:45.546570+00:00"},{"alias_kind":"pith_short_16","alias_value":"RCTDGZQNHXPIBJHU","created_at":"2026-07-05T09:37:45.546570+00:00"},{"alias_kind":"pith_short_8","alias_value":"RCTDGZQN","created_at":"2026-07-05T09:37:45.546570+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/RCTDGZQNHXPIBJHULHRZGE24AW","json":"https://pith.science/pith/RCTDGZQNHXPIBJHULHRZGE24AW.json","graph_json":"https://pith.science/api/pith-number/RCTDGZQNHXPIBJHULHRZGE24AW/graph.json","events_json":"https://pith.science/api/pith-number/RCTDGZQNHXPIBJHULHRZGE24AW/events.json","paper":"https://pith.science/paper/RCTDGZQN"},"agent_actions":{"view_html":"https://pith.science/pith/RCTDGZQNHXPIBJHULHRZGE24AW","download_json":"https://pith.science/pith/RCTDGZQNHXPIBJHULHRZGE24AW.json","view_paper":"https://pith.science/paper/RCTDGZQN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.12609&json=true","fetch_graph":"https://pith.science/api/pith-number/RCTDGZQNHXPIBJHULHRZGE24AW/graph.json","fetch_events":"https://pith.science/api/pith-number/RCTDGZQNHXPIBJHULHRZGE24AW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RCTDGZQNHXPIBJHULHRZGE24AW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RCTDGZQNHXPIBJHULHRZGE24AW/action/storage_attestation","attest_author":"https://pith.science/pith/RCTDGZQNHXPIBJHULHRZGE24AW/action/author_attestation","sign_citation":"https://pith.science/pith/RCTDGZQNHXPIBJHULHRZGE24AW/action/citation_signature","submit_replication":"https://pith.science/pith/RCTDGZQNHXPIBJHULHRZGE24AW/action/replication_record"}},"created_at":"2026-07-05T09:37:45.546570+00:00","updated_at":"2026-07-05T09:37:45.546570+00:00"}