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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1512.09249","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-31T10:15:06Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"5eed1843478d3ac8f1c26bff8a3b698fdc53dcf92a76f21d2fcec8508f6fe8f6","abstract_canon_sha256":"a7dcb430c2c713213faaf5540d1318f23bb7096343f383b4825282870eb4bafd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:32.883571Z","signature_b64":"OnUHHFq/qGZ+lfPy1u9hVAaJOferD6N275+3nKCjTYsVZoYubamP7XdED02WHcrsttLl+HEUHm670QSZ4vQbBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"791fa0e9b5ef8ad301c4f507c2a179daca6b04eec04d45b0e2db1da4ce81dc18","last_reissued_at":"2026-05-18T01:23:32.882829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:32.882829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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