{"paper":{"title":"Towards the Jacquet Conjecture on the Local Converse Problem for $p$-adic $\\mathrm{GL}_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Chufeng Nien, Dihua Jiang, Shaun Stevens","submitted_at":"2015-04-11T00:43:53Z","abstract_excerpt":"The Local Converse Problem is to determine how the family of the local gamma factors $\\gamma(s,\\pi\\times\\tau,\\psi)$ characterizes the isomorphism class of an irreducible admissible generic representation $\\pi$ of $\\mathrm{GL}_n(F)$, with $F$ a non-archimedean local field, where $\\tau$ runs through all irreducible supercuspidal representations of $\\mathrm{GL}_r(F)$ and $r$ runs through positive integers. The Jacquet conjecture asserts that it is enough to take $r=1,2,\\ldots,\\left[\\frac{n}{2}\\right]$. Based on arguments in the work of Henniart and of Chen giving preliminary steps towards the Jac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02819","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"}