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In this paper, we prove that there is a constant $ \\gamma (Q) $ expressed as a certain Euler product associated to $Q$ such that at least $ \\gamma (Q) / 11 $ of the Rankin--Selberg special $L$-values $L (1/2+it_j, Q \\otimes u_j)$ for $ t_j \\leqslant T$ do not vanish as $T \\rightarrow \\infty$. Further, we show that the non-vanishing proportion is at least $\\gamma (Q) \\cdot (4\\mu-3) / (4\\m"},"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":"2506.08546","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-06-10T08:12:05Z","cross_cats_sorted":[],"title_canon_sha256":"39135e4307eb2fb89fb5f8ce974dee8c6d4429eb5ef84e211d48c0e12ef5ce33","abstract_canon_sha256":"8014664514736b9ced53cf8f91479066c5780d92bcae2a5cd231058b0eff3768"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:39:54.940963Z","signature_b64":"wWfIOmZa7s4WCQ1PiTaQcgYuuIBaOPo1OnrlthkLElUyaSTJmW+hUleWZV0UrVJqU2RH3eDLljpyCRBsJaHqCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f983d65ea4e51bcc00a9828a9e19cb1c7729dc6189035631a71ff62c202088b7","last_reissued_at":"2026-07-05T11:39:54.940551Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:39:54.940551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Effective Non-vanishing of Rankin--Selberg $L$-functions at Special Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Zhi Qi","submitted_at":"2025-06-10T08:12:05Z","abstract_excerpt":"Let $Q (z)$ be a holomorphic Hecke cusp newform of square-free level and $u_j (z)$ traverse an orthonormal basis of Hecke--Maass cusp forms of full level. Let $1/4 + t_j^2$ be the Laplace eigenvalue $u_j (z)$. In this paper, we prove that there is a constant $ \\gamma (Q) $ expressed as a certain Euler product associated to $Q$ such that at least $ \\gamma (Q) / 11 $ of the Rankin--Selberg special $L$-values $L (1/2+it_j, Q \\otimes u_j)$ for $ t_j \\leqslant T$ do not vanish as $T \\rightarrow \\infty$. Further, we show that the non-vanishing proportion is at least $\\gamma (Q) \\cdot (4\\mu-3) / (4\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08546","kind":"arxiv","version":3},"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/2506.08546/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":"2506.08546","created_at":"2026-07-05T11:39:54.940612+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.08546v3","created_at":"2026-07-05T11:39:54.940612+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08546","created_at":"2026-07-05T11:39:54.940612+00:00"},{"alias_kind":"pith_short_12","alias_value":"7GB5MXVE4UN4","created_at":"2026-07-05T11:39:54.940612+00:00"},{"alias_kind":"pith_short_16","alias_value":"7GB5MXVE4UN4YAFJ","created_at":"2026-07-05T11:39:54.940612+00:00"},{"alias_kind":"pith_short_8","alias_value":"7GB5MXVE","created_at":"2026-07-05T11:39:54.940612+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.14566","citing_title":"On the Effective Non-vanishing of Hecke--Maass $L$-functions at Special Points","ref_index":28,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7GB5MXVE4UN4YAFJQKFJ4GOLDR","json":"https://pith.science/pith/7GB5MXVE4UN4YAFJQKFJ4GOLDR.json","graph_json":"https://pith.science/api/pith-number/7GB5MXVE4UN4YAFJQKFJ4GOLDR/graph.json","events_json":"https://pith.science/api/pith-number/7GB5MXVE4UN4YAFJQKFJ4GOLDR/events.json","paper":"https://pith.science/paper/7GB5MXVE"},"agent_actions":{"view_html":"https://pith.science/pith/7GB5MXVE4UN4YAFJQKFJ4GOLDR","download_json":"https://pith.science/pith/7GB5MXVE4UN4YAFJQKFJ4GOLDR.json","view_paper":"https://pith.science/paper/7GB5MXVE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.08546&json=true","fetch_graph":"https://pith.science/api/pith-number/7GB5MXVE4UN4YAFJQKFJ4GOLDR/graph.json","fetch_events":"https://pith.science/api/pith-number/7GB5MXVE4UN4YAFJQKFJ4GOLDR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7GB5MXVE4UN4YAFJQKFJ4GOLDR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7GB5MXVE4UN4YAFJQKFJ4GOLDR/action/storage_attestation","attest_author":"https://pith.science/pith/7GB5MXVE4UN4YAFJQKFJ4GOLDR/action/author_attestation","sign_citation":"https://pith.science/pith/7GB5MXVE4UN4YAFJQKFJ4GOLDR/action/citation_signature","submit_replication":"https://pith.science/pith/7GB5MXVE4UN4YAFJQKFJ4GOLDR/action/replication_record"}},"created_at":"2026-07-05T11:39:54.940612+00:00","updated_at":"2026-07-05T11:39:54.940612+00:00"}