{"paper":{"title":"A rationality result for the exterior and the symmetric square $L$-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Harald Grobner","submitted_at":"2014-12-27T21:49:27Z","abstract_excerpt":"Let $G={\\rm GL}_{2n}$ over a totally real number field $F$ and $n\\geq 2$. Let $\\Pi$ be a cuspidal automorphic representation of $G(\\mathbb A)$, which is cohomological and a functorial lift from SO$(2n+1)$. The latter condition can be equivalently reformulated that the exterior square $L$-function of $\\Pi$ has a pole at $s=1$. In this paper, we prove a rationality result for the residue of the exterior square $L$-function at $s=1$ and also for the holomorphic value of the symmetric square $L$-function at $s=1$ attached to $\\Pi$. On the way, we also show a rationality result for the residue of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8082","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"}