{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PIYJJR7KV2LXVTRYUACNWZY6IQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"86427db1b639258d3454589e748ca8dec57651dbdf73a06e0732150f123234f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-05T16:21:59Z","title_canon_sha256":"44b6cf11183ac2a6e9070888c34d329f01e03d7466971e2caead2843b941fca0"},"schema_version":"1.0","source":{"id":"1510.01208","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.01208","created_at":"2026-05-18T01:31:04Z"},{"alias_kind":"arxiv_version","alias_value":"1510.01208v1","created_at":"2026-05-18T01:31:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01208","created_at":"2026-05-18T01:31:04Z"},{"alias_kind":"pith_short_12","alias_value":"PIYJJR7KV2LX","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PIYJJR7KV2LXVTRY","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PIYJJR7K","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:77bb8865605f1f366e227a5ede2c691cf306b35232734d1ff0ba6d82327adfd7","target":"graph","created_at":"2026-05-18T01:31:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $\\pi$ be a unitary automorphic cuspidal representation of $GL_2(\\mathbb{Q}_\\mathbb{A})$ with Fourier coefficients $\\lambda_\\pi(n)$. Asymptotic expansions of certain sums of $\\lambda_\\pi(n)$ are proved using known functorial liftings from $GL_2$, including symmetric powers, isobaric sums, exterior square from $GL_4$ and base change. These asymptotic expansions are manifestation of the underlying functoriality and reflect value distribution of $\\lambda_\\pi(n)$ on integers, squares, cubes and fourth powers.","authors_text":"Huixue Lao, Mark McKee, Yangbo Ye","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-05T16:21:59Z","title":"Asymptotics for cuspidal representations by functoriality from GL(2)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01208","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:05d0e869862c98d816968b07654ce2b4076af10a42f194129bcefce81bfb883a","target":"record","created_at":"2026-05-18T01:31:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"86427db1b639258d3454589e748ca8dec57651dbdf73a06e0732150f123234f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-05T16:21:59Z","title_canon_sha256":"44b6cf11183ac2a6e9070888c34d329f01e03d7466971e2caead2843b941fca0"},"schema_version":"1.0","source":{"id":"1510.01208","kind":"arxiv","version":1}},"canonical_sha256":"7a3094c7eaae977ace38a004db671e4422d75eb31b2cbeab32e9651569e82cde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a3094c7eaae977ace38a004db671e4422d75eb31b2cbeab32e9651569e82cde","first_computed_at":"2026-05-18T01:31:04.562358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:04.562358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FJj2WlxvMDfaVI5sYoh27k0Aj/YelN/RGasTUNgxv3CmJWzXdEQjUEoyDUxYFBbf6GKoxTjk3f6CgdJecAH7Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:04.563132Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.01208","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05d0e869862c98d816968b07654ce2b4076af10a42f194129bcefce81bfb883a","sha256:77bb8865605f1f366e227a5ede2c691cf306b35232734d1ff0ba6d82327adfd7"],"state_sha256":"8dac8ab0207784dfcce00f96d348feb9fc8e516032280b52e1bca48a59e2d60a"}