{"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"}