{"paper":{"title":"Subconvexity for twisted $L$-functions on $\\mathrm{GL}_3$ over the Gaussian number field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Zhi Qi","submitted_at":"2018-05-15T20:26:25Z","abstract_excerpt":"Let $q \\in \\mathbb{Z} [i]$ be prime and $\\chi $ be the primitive quadratic Hecke character modulo $q$. Let $\\pi$ be a self-dual Hecke automorphic cusp form for $\\mathrm{SL}_3 (\\mathbb{Z} [i] )$ and $f$ be a Hecke cusp form for $\\Gamma_0 (q) \\subset \\mathrm{SL}_2 (\\mathbb{Z} [i])$. Consider the twisted $L$-functions $ L (s, \\pi \\otimes f \\otimes \\chi) $ and $L (s, \\pi \\otimes \\chi)$ on $\\mathrm{GL}_3 \\times \\mathrm{GL}_2$ and $\\mathrm{GL}_3$. We prove the subconvexity bounds\n  \\begin{equation*}\n  L \\big(\\tfrac 1 2, \\pi \\otimes f \\otimes \\chi \\big) \\ll_{\\, \\varepsilon, \\pi, f } \\mathrm{N} (q)^{5"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06026","kind":"arxiv","version":4},"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"}