{"paper":{"title":"A local converse theorem for U(1,1)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Qing Zhang","submitted_at":"2015-08-28T00:37:23Z","abstract_excerpt":"In this paper, we define a $\\gamma$-factor for generic representations of $\\RU(1,1)\\times \\Res_{E/F}(\\GL_1)$ and prove a local converse theorem for $\\RU(1,1)$ using the $\\gamma$-factor we defined. We also give a new proof of the local converse theorem for $\\GL_2$ using a $\\gamma$-factor of $\\GL_2\\times \\GL_2$ type which was originally defined by Jacquet in \\cite{J}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07062","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"}