{"paper":{"title":"Characterisation of the poles of the $\\ell$-modular Asai $L$-factor","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":"2019-03-06T14:49:44Z","abstract_excerpt":"Let $E/F$ be a quadratic extension of non-archimedean local fields, and let $\\ell$ be a prime number different from the residual characteristic of $F$. For a complex cuspidal representation $\\pi$ of $GL(n,E)$, the Asai $L$-factor $L^+(X,\\pi)$ has a pole at $X=1$ if and only if $\\pi$ is $GL(n,F)$-distinguished. In this paper we solve the problem of characterising the occurrence of a pole at $X=1$ of $L^+(X,\\pi)$ when $\\pi$ is an $\\ell$-modular cuspidal representation of $GL(n,E)$: we show that $L^+(X,\\pi)$ has a pole at $X=1$ if and only if $\\pi$ is a relatively banal distinguished representati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02427","kind":"arxiv","version":3},"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"}