{"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. Let $L(s,\\pi\\otimes \\chi)$ be the $L$-function associated to $\\pi\\otimes \\chi$. 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"}