{"paper":{"title":"The circle method and bounds for $L$-functions - IV: Subconvexity for twists of $GL(3)$ $L$-functions - B","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ritabrata Munshi","submitted_at":"2013-11-24T13:44:56Z","abstract_excerpt":"Let $\\pi$ be a $SL(3,\\mathbb Z)$ Hecke-Maass cusp form satisfying the Ramanujan conjecture and the Selberg-Ramanujan conjecture, and let $\\chi$ be a primitive Dirichlet character modulo $M$, which we assume to be prime for simplicity. We will prove the following subconvex bound $$ L\\left(\\tfrac{1}{2},\\pi\\otimes\\chi\\right)\\ll_{\\pi,\\varepsilon} M^{\\frac{3}{4}-\\frac{1}{1612}+\\varepsilon}. $$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6120","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"}