{"paper":{"title":"Test vectors for local cuspidal Rankin-Selberg integrals of GL(n), and reduction modulo $\\ell$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Nadir Matringe, Robert Kurinczuk","submitted_at":"2015-01-29T20:48:13Z","abstract_excerpt":"Let $\\pi_1,\\pi_2$ be a pair of cuspidal complex, or $\\ell$-adic, representations of the general linear group of rank $n$ over a non-archimedean local field $F$ of residual characteristic $p$, different to $\\ell$. Whenever the local Rankin-Selberg $L$-factor $L(X,\\pi_1,\\pi_2)$ is nontrivial, we exhibit explicit test vectors in the Whittaker models of $\\pi_1$ and $\\pi_2$ such that the local Rankin-Selberg integral associated to these vectors and to the characteristic function of $\\mathfrak{o}_F^n$ is equal to $L(X,\\pi_1,\\pi_2)$. We give an initial application of the test vectors to reduction mod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07587","kind":"arxiv","version":4},"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"}