{"paper":{"title":"Transfer of Siegel cusp forms of degree 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Abhishek Saha, Ameya Pitale, Ralf Schmidt","submitted_at":"2011-06-28T10:05:00Z","abstract_excerpt":"Let $\\pi$ be the automorphic representation of $\\GSp_4(\\A)$ generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and $\\tau$ be an arbitrary cuspidal, automorphic representation of $\\GL_2(\\A)$. Using Furusawa's integral representation for $\\GSp_4\\times\\GL_2$ combined with a pullback formula involving the unitary group $\\GU(3,3)$, we prove that the $L$-functions $L(s,\\pi\\times\\tau)$ are \"nice\". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations $\\pi$ have a functorial lifting to a cuspidal representation of $\\GL_4(\\A)$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5611","kind":"arxiv","version":3},"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"}