{"paper":{"title":"Beyond Endoscopy via the trace formula - III: The standard representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Salim Ali Altug","submitted_at":"2015-12-31T10:15:06Z","abstract_excerpt":"We finalize the analysis of the trace formula initiated in \\cite{Altug:2015aa} and developed in \\cite{Altug:2015ab}, and calculate the asymptotic expansion of the beyond endoscopic averages for the standard $L$-functions attached to weight $k\\geq3$ cusp forms on $GL(2)$ (cf. Theorem \\ref{mainthm}). This, in particular, constitutes the first example of beyond endoscopy executed via the Arthur-Selberg trace formula, as originally proposed in \\cite{Langlands:2004aa}. As an application we also give a new proof of the analytic continuation of the $L$-function attached to Ramanujan's $\\Delta$-functi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09249","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"}