{"paper":{"title":"A local converse theorem for $\\textrm{U}_{2r+1}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Qing Zhang","submitted_at":"2017-05-26T02:00:21Z","abstract_excerpt":"Let $E/F$ be a quadratic extension of $p$-adic fields and $\\textrm{U}_{2r+1}$ be the unitary group associated with $E/F$. We prove the following local converse theorem for $\\textrm{U}_{2r+1}$: given two irreducible generic supercuspidal representations $\\pi,\\pi_0$ of $\\textrm{U}_{2r+1}$ with the same central character, if $\\gamma(s,\\pi\\times \\tau,\\psi)=\\gamma(s,\\pi_0\\times \\tau,\\psi)$ for all irreducible generic representation $\\tau$ of $\\textrm{GL}_n(E)$ and for all $n$ with $1\\le n\\le r$, then $\\pi\\cong \\pi_0$. The proof depends on analysis of the local integrals which define local gamma fac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09410","kind":"arxiv","version":2},"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"}