{"paper":{"title":"Discrete series multiplicities for classical groups over Z and level 1 algebraic cusp forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.NT","authors_text":"Ga\\\"etan Chenevier, Olivier Ta\\\"ibi","submitted_at":"2019-07-20T09:17:01Z","abstract_excerpt":"The aim of this paper is twofold. First, we introduce a new method for evaluating the multiplicity of a given discrete series in the space of level $1$ automorphic forms of a split classical group $G$ over $\\mathbb{Z}$, and provide numerical applications in absolute rank $\\leq 8$. Second, we prove a classification result for the level one cuspidal algebraic automorphic representations of ${\\rm GL}_n$ over $\\mathbb{Q}$ ($n$ arbitrary) whose motivic weight is $\\leq 24$.\n  In both cases, a key ingredient is a classical method based on the Weil explicit formula, which allows to disprove the existe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08783","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"}