{"paper":{"title":"Hybrid subconvexity bounds for $L \\left(\\tfrac{1}{2}, \\text{Sym}^2 f \\otimes g\\right)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ritabrata Munshi, Roman Holowinsky, Zhi Qi","submitted_at":"2014-01-26T21:44:40Z","abstract_excerpt":"Fix an integer $\\kappa\\geqslant 2$. Let $P$ be prime and let $k> \\kappa$ be an even integer. For $f$ a holomorphic cusp form of weight $k$ and full level and $g$ a primitive holomorphic cusp form of weight $2 \\kappa$ and level $P$, we prove hybrid subconvexity bounds for $L \\left(\\tfrac{1}{2}, \\text{Sym}^2 f \\otimes g\\right)$ in the $k$ and $P$ aspects when $P^{\\frac {13} {64} + \\delta} < k < P^{\\frac 3 8 - \\delta}$ for any $0 < \\delta < \\frac {11} {128}$. These bounds are achieved through a first moment method (with amplification when $P^{\\frac {13} {64}} < k \\leqslant P^{\\frac 4 {13}}$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6695","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"}