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In this paper, for any given $\\varepsilon>0$, we establish a subconvex bound $L(1/2+it, \\pi\\otimes \\chi)\\ll_{\\pi, \\varepsilon} (M(|t|+1))^{3/4-1/36+\\varepsilon}$, uniformly in both the $M$- and $t$-aspects."},"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":"1802.05111","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-14T14:36:10Z","cross_cats_sorted":[],"title_canon_sha256":"2322f4cdabc186e730b5bd359e5c631fbd7d5a2911e17d3444316b288221161a","abstract_canon_sha256":"9ace760ce6854bcdafb0ec893798050e9d175f51dd72d0e09e02861a3b20fa4e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:58:23.312193Z","signature_b64":"b3CBFYpVMDJb0v26veRugr07aifK1DjUiA8j462Ck7erVBrQokatWIDJTSs8bCpXqGZljzQsWJmEpLZCS5ugBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d41444533e1874cd9ace0cdf2eedc22bb7cbc9d86cb37934bccafd7c79cc64c","last_reissued_at":"2026-07-05T00:58:23.311798Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:58:23.311798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounds for twists of $\\rm GL(3)$ $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yongxiao Lin","submitted_at":"2018-02-14T14:36:10Z","abstract_excerpt":"Let $\\pi$ be a fixed Hecke--Maass cusp form for $\\mathrm{SL}(3,\\mathbb{Z})$ and $\\chi$ be a primitive Dirichlet character modulo $M$, which we assume to be a prime. 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In this paper, for any given $\\varepsilon>0$, we establish a subconvex bound $L(1/2+it, \\pi\\otimes \\chi)\\ll_{\\pi, \\varepsilon} (M(|t|+1))^{3/4-1/36+\\varepsilon}$, uniformly in both the $M$- and $t$-aspects."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.05111","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1802.05111/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":"1802.05111","created_at":"2026-07-05T00:58:23.311860+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.05111v2","created_at":"2026-07-05T00:58:23.311860+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.05111","created_at":"2026-07-05T00:58:23.311860+00:00"},{"alias_kind":"pith_short_12","alias_value":"TVAUIRJT4GDU","created_at":"2026-07-05T00:58:23.311860+00:00"},{"alias_kind":"pith_short_16","alias_value":"TVAUIRJT4GDUZWNM","created_at":"2026-07-05T00:58:23.311860+00:00"},{"alias_kind":"pith_short_8","alias_value":"TVAUIRJT","created_at":"2026-07-05T00:58:23.311860+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/TVAUIRJT4GDUZWNM4DG7F3W4EK","json":"https://pith.science/pith/TVAUIRJT4GDUZWNM4DG7F3W4EK.json","graph_json":"https://pith.science/api/pith-number/TVAUIRJT4GDUZWNM4DG7F3W4EK/graph.json","events_json":"https://pith.science/api/pith-number/TVAUIRJT4GDUZWNM4DG7F3W4EK/events.json","paper":"https://pith.science/paper/TVAUIRJT"},"agent_actions":{"view_html":"https://pith.science/pith/TVAUIRJT4GDUZWNM4DG7F3W4EK","download_json":"https://pith.science/pith/TVAUIRJT4GDUZWNM4DG7F3W4EK.json","view_paper":"https://pith.science/paper/TVAUIRJT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.05111&json=true","fetch_graph":"https://pith.science/api/pith-number/TVAUIRJT4GDUZWNM4DG7F3W4EK/graph.json","fetch_events":"https://pith.science/api/pith-number/TVAUIRJT4GDUZWNM4DG7F3W4EK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TVAUIRJT4GDUZWNM4DG7F3W4EK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TVAUIRJT4GDUZWNM4DG7F3W4EK/action/storage_attestation","attest_author":"https://pith.science/pith/TVAUIRJT4GDUZWNM4DG7F3W4EK/action/author_attestation","sign_citation":"https://pith.science/pith/TVAUIRJT4GDUZWNM4DG7F3W4EK/action/citation_signature","submit_replication":"https://pith.science/pith/TVAUIRJT4GDUZWNM4DG7F3W4EK/action/replication_record"}},"created_at":"2026-07-05T00:58:23.311860+00:00","updated_at":"2026-07-05T00:58:23.311860+00:00"}