{"paper":{"title":"Characterization of \\gamma-factors: the Asai case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Guy Henniart, Luis Lomel\\'i","submitted_at":"2009-10-16T14:34:15Z","abstract_excerpt":"Let $E$ be a separable quadratic extension of a locally compact field $F$ of positive characteristic. Asai \\gamma-factors are defined for smooth irreducible representations \\pi of ${\\rm GL}_n(E)$. If \\sigma is the Weil-Deligne representation of $\\mathcal{W}_E$ corresponding to \\pi under the local Langlands correspondence, we show that the Asai \\gamma-factor is the same as the Deligne-Langlands \\gamma-factor of the Weil-Deligne representation of $\\mathcal{W}_F$ obtained from \\sigma under tensor induction. This is achieved by proving that Asai \\gamma-factors are characterized by their local prop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.3128","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"}