{"paper":{"title":"Sato-Tate theorem for families and low-lying zeros of automorphic $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO","math.RT"],"primary_cat":"math.NT","authors_text":"Nicolas Templier, Sug Woo Shin","submitted_at":"2012-08-09T15:19:07Z","abstract_excerpt":"We consider certain families of automorphic representations over number fields arising from the principle of functoriality of Langlands. Let $G$ be a reductive group over a number field $F$ which admits discrete series representations at infinity. Let $^{L}G=\\hat G \\rtimes \\mathrm{Gal}(\\bar F/F)$ be the associated $L$-group and $r:{}^L G\\to \\mathrm{GL}(d,\\mathbb{C})$ a continuous homomorphism which is irreducible and does not factor through $\\mathrm{Gal}(\\bar F/F)$. The families under consideration consist of discrete automorphic representations of $G(\\mathbb{A}_F)$ of given weight and level a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1945","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"}