{"paper":{"title":"Hybrid subconvexity bounds for twisted $L$-functions on $GL(3)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bingrong Huang","submitted_at":"2016-05-31T04:07:01Z","abstract_excerpt":"Let $q$ be a large prime, and $\\chi$ the quadratic character modulo $q$. Let $\\phi$ be a self-dual Hecke--Maass cusp form for $SL(3,\\mathbb{Z})$, and $u_j$ a Hecke--Maass cusp form for $\\Gamma_0(q)\\subseteq SL(2,\\mathbb{Z})$ with spectral parameter $t_j$. We prove the hybrid subconvexity bounds for the twisted $L$-functions \\[ L(1/2,\\phi\\times u_j\\times\\chi)\\ll_{\\phi,\\varepsilon} (qt_j)^{3/2-\\theta+\\varepsilon},\\quad L(1/2+it,\\phi\\times\\chi)\\ll_{\\phi,\\varepsilon} (qt)^{3/4-\\theta/2+\\varepsilon}, \\] for any $\\varepsilon>0$, where $\\theta=1/23$ is admissible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09487","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"}