{"paper":{"title":"Bounds for $GL_3$ $L$-functions in depth aspect","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Qingfeng Sun, Rui Zhao","submitted_at":"2018-03-29T09:15:58Z","abstract_excerpt":"Let $f$ be a Hecke-Maass cusp form for $SL_3(\\mathbb{Z})$ and $\\chi$ a primitive Dirichlet character of prime power conductor $\\mathfrak{q}=p^{\\kappa}$ with $p$ prime and $\\kappa\\geq 10$. We prove a subconvexity bound $$ L\\left(\\frac{1}{2},\\pi\\otimes \\chi\\right)\\ll_{p,\\pi,\\varepsilon} \\mathfrak{q}^{3/4-3/40+\\varepsilon} $$ for any $\\varepsilon>0$, where the dependence of the implied constant on $p$ is explicit and polynomial. We obtain this result by applying the circle method of Kloosterman's version, summation formulas of Poisson and Voronoi's type and a conductor lowering mechanism introduc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10973","kind":"arxiv","version":1},"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"}