{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:H7L5VYAUZ4SXE5ZNAGFLYG73YK","short_pith_number":"pith:H7L5VYAU","schema_version":"1.0","canonical_sha256":"3fd7dae014cf2572772d018abc1bfbc2b0a15479f4121dacf716540d65971d4c","source":{"kind":"arxiv","id":"2403.13895","version":1},"attestation_state":"computed","paper":{"title":"Quotients of $L$-functions: degrees $n$ and $n-2$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ravi Raghunathan","submitted_at":"2024-03-20T18:06:37Z","abstract_excerpt":"If $L(s,\\pi)$ and $L(s,\\rho)$ are the Dirichlet series attached to cuspidal automorphic representations $\\pi$ and $\\rho$ of ${\\rm GL}_n({\\mathbb A}_{\\mathbb Q})$ and ${\\rm GL}_{n-2}({\\mathbb A}_{\\mathbb Q})$ respectively, we show that $F_2(s)=L(s,\\pi)/L(s,\\rho)$ has infinitely many poles.\n  We also establish analogous results for Artin $L$-functions and other $L$-functions not yet proven to be automorphic. Using the classification theorems of \\cite{Ragh20} and \\cite{BaRa20}, we show that cuspidal $L$-functions of ${\\rm GL}_3({\\mathbb A}_{\\mathbb Q})$ are primitive in ${\\mathfrak G}$, a monoid "},"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":"2403.13895","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-03-20T18:06:37Z","cross_cats_sorted":[],"title_canon_sha256":"4dae7a764177b91b819267d327a19cdf4478ed484a6f65218eaca96deae217a8","abstract_canon_sha256":"6cc36c384d2989f9fcc077bcc8c9609587e21cb1e12e09d11d299c2f14f6396e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:58:51.590205Z","signature_b64":"OOH9wyY+rgQ1z71ddG1vuKU/BellGWAkj/Jx1yD1vUDa7FkQEEjADxZfIFbVYUDoLSDlN6tG+Y4/5A9iWGS7DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fd7dae014cf2572772d018abc1bfbc2b0a15479f4121dacf716540d65971d4c","last_reissued_at":"2026-07-05T07:58:51.589711Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:58:51.589711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quotients of $L$-functions: degrees $n$ and $n-2$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ravi Raghunathan","submitted_at":"2024-03-20T18:06:37Z","abstract_excerpt":"If $L(s,\\pi)$ and $L(s,\\rho)$ are the Dirichlet series attached to cuspidal automorphic representations $\\pi$ and $\\rho$ of ${\\rm GL}_n({\\mathbb A}_{\\mathbb Q})$ and ${\\rm GL}_{n-2}({\\mathbb A}_{\\mathbb Q})$ respectively, we show that $F_2(s)=L(s,\\pi)/L(s,\\rho)$ has infinitely many poles.\n  We also establish analogous results for Artin $L$-functions and other $L$-functions not yet proven to be automorphic. Using the classification theorems of \\cite{Ragh20} and \\cite{BaRa20}, we show that cuspidal $L$-functions of ${\\rm GL}_3({\\mathbb A}_{\\mathbb Q})$ are primitive in ${\\mathfrak G}$, a monoid "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.13895","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/2403.13895/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":"2403.13895","created_at":"2026-07-05T07:58:51.589772+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.13895v1","created_at":"2026-07-05T07:58:51.589772+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.13895","created_at":"2026-07-05T07:58:51.589772+00:00"},{"alias_kind":"pith_short_12","alias_value":"H7L5VYAUZ4SX","created_at":"2026-07-05T07:58:51.589772+00:00"},{"alias_kind":"pith_short_16","alias_value":"H7L5VYAUZ4SXE5ZN","created_at":"2026-07-05T07:58:51.589772+00:00"},{"alias_kind":"pith_short_8","alias_value":"H7L5VYAU","created_at":"2026-07-05T07:58:51.589772+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/H7L5VYAUZ4SXE5ZNAGFLYG73YK","json":"https://pith.science/pith/H7L5VYAUZ4SXE5ZNAGFLYG73YK.json","graph_json":"https://pith.science/api/pith-number/H7L5VYAUZ4SXE5ZNAGFLYG73YK/graph.json","events_json":"https://pith.science/api/pith-number/H7L5VYAUZ4SXE5ZNAGFLYG73YK/events.json","paper":"https://pith.science/paper/H7L5VYAU"},"agent_actions":{"view_html":"https://pith.science/pith/H7L5VYAUZ4SXE5ZNAGFLYG73YK","download_json":"https://pith.science/pith/H7L5VYAUZ4SXE5ZNAGFLYG73YK.json","view_paper":"https://pith.science/paper/H7L5VYAU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.13895&json=true","fetch_graph":"https://pith.science/api/pith-number/H7L5VYAUZ4SXE5ZNAGFLYG73YK/graph.json","fetch_events":"https://pith.science/api/pith-number/H7L5VYAUZ4SXE5ZNAGFLYG73YK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H7L5VYAUZ4SXE5ZNAGFLYG73YK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H7L5VYAUZ4SXE5ZNAGFLYG73YK/action/storage_attestation","attest_author":"https://pith.science/pith/H7L5VYAUZ4SXE5ZNAGFLYG73YK/action/author_attestation","sign_citation":"https://pith.science/pith/H7L5VYAUZ4SXE5ZNAGFLYG73YK/action/citation_signature","submit_replication":"https://pith.science/pith/H7L5VYAUZ4SXE5ZNAGFLYG73YK/action/replication_record"}},"created_at":"2026-07-05T07:58:51.589772+00:00","updated_at":"2026-07-05T07:58:51.589772+00:00"}