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In this paper we will prove the following subconvex bound $$ L(\\t1/2,\\pi\\otimes\\chi)\\ll_{\\pi,\\varepsilon} M^{3/4}-\\delta+\\varepsilon}. $$"},"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":"1211.5731","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-25T06:19:17Z","cross_cats_sorted":[],"title_canon_sha256":"5c0d63a189b2fa507d626e453de5a6754fe18e895cca9eab2374ef0d1d4347c0","abstract_canon_sha256":"2fc2d1d69b088663da6003e8acb523184c4e76fb0f7e13f2a696f97087910fcf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:06.152887Z","signature_b64":"3NN0YUPl8cqRDUpF4Zu5Hs7FfQ290JLZf3ApduVeqC1c2BEfZ4bSNtd+jjP7ST3y3FBQD8rAV2s314apsTYVCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c527934fd2385941ba11dc9aef336620f9a983787fef6cccf5e89038d19769f3","last_reissued_at":"2026-05-18T03:36:06.152376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:06.152376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The circle method and bounds for $L$-functions - II: Subconvexity for twists of GL(3) $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ritabrata Munshi","submitted_at":"2012-11-25T06:19:17Z","abstract_excerpt":"Let $\\pi$ be a $SL(3,\\mathbb Z)$ automorphic form. Let $\\chi=\\chi_1\\chi_2$ be a Dirichlet character with $\\chi_i$ primitive modulo $M_i$. Suppose $M_1$, $M_2$ are primes such that $\\sqrt{M_2}M^{4\\delta}<M_1<M_2M^{-3\\delta}$, where $M=M_1M_2$ and $0<\\delta<1/28$. In this paper we will prove the following subconvex bound $$ L(\\t1/2,\\pi\\otimes\\chi)\\ll_{\\pi,\\varepsilon} M^{3/4}-\\delta+\\varepsilon}. $$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5731","kind":"arxiv","version":2},"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":"1211.5731","created_at":"2026-05-18T03:36:06.152446+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.5731v2","created_at":"2026-05-18T03:36:06.152446+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5731","created_at":"2026-05-18T03:36:06.152446+00:00"},{"alias_kind":"pith_short_12","alias_value":"YUTZGT6SHBMU","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"YUTZGT6SHBMUDOQR","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"YUTZGT6S","created_at":"2026-05-18T12:27:30.460161+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/YUTZGT6SHBMUDOQR3SNO6M3GED","json":"https://pith.science/pith/YUTZGT6SHBMUDOQR3SNO6M3GED.json","graph_json":"https://pith.science/api/pith-number/YUTZGT6SHBMUDOQR3SNO6M3GED/graph.json","events_json":"https://pith.science/api/pith-number/YUTZGT6SHBMUDOQR3SNO6M3GED/events.json","paper":"https://pith.science/paper/YUTZGT6S"},"agent_actions":{"view_html":"https://pith.science/pith/YUTZGT6SHBMUDOQR3SNO6M3GED","download_json":"https://pith.science/pith/YUTZGT6SHBMUDOQR3SNO6M3GED.json","view_paper":"https://pith.science/paper/YUTZGT6S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.5731&json=true","fetch_graph":"https://pith.science/api/pith-number/YUTZGT6SHBMUDOQR3SNO6M3GED/graph.json","fetch_events":"https://pith.science/api/pith-number/YUTZGT6SHBMUDOQR3SNO6M3GED/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YUTZGT6SHBMUDOQR3SNO6M3GED/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YUTZGT6SHBMUDOQR3SNO6M3GED/action/storage_attestation","attest_author":"https://pith.science/pith/YUTZGT6SHBMUDOQR3SNO6M3GED/action/author_attestation","sign_citation":"https://pith.science/pith/YUTZGT6SHBMUDOQR3SNO6M3GED/action/citation_signature","submit_replication":"https://pith.science/pith/YUTZGT6SHBMUDOQR3SNO6M3GED/action/replication_record"}},"created_at":"2026-05-18T03:36:06.152446+00:00","updated_at":"2026-05-18T03:36:06.152446+00:00"}