{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6CYSL2KZ7UJGBHQ3CMNRPE2K4T","short_pith_number":"pith:6CYSL2KZ","schema_version":"1.0","canonical_sha256":"f0b125e959fd12609e1b131b17934ae4d1e7656de9287a608c66eaf252a15357","source":{"kind":"arxiv","id":"1506.07416","version":1},"attestation_state":"computed","paper":{"title":"Central limit theorem for Artin $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Henry H. Kim, Peter J. Cho","submitted_at":"2015-06-24T15:13:27Z","abstract_excerpt":"We show that the sum of the traces of Frobenius elements of Artin $L$-functions in a family of $G$-fields satisfies the Gaussian distribution under certain counting conjectures. We prove the counting conjectures for $S_4$ and $S_5$-fields. We also show central limit theorem for modular form $L$-functions with the trivial central character with respect to congruence subgroups as the level goes to infinity."},"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":"1506.07416","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-24T15:13:27Z","cross_cats_sorted":[],"title_canon_sha256":"c04d09c25d43b310985a99c374555752c479b594d03e68a3472fe4dd2d8441fe","abstract_canon_sha256":"f7a83a216df2f18ef4ea0346be9f8d5270847085c6a2e59fd7e7ab3a5b09ac03"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:54.104713Z","signature_b64":"y/vNkgCqkhODzqoaOXaX6tgpqATRJs9ATbSa5swEcQSKBXSi1wflHgnae5KtlN1e9c7YQ89GeZ3d7RsBlYx9AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0b125e959fd12609e1b131b17934ae4d1e7656de9287a608c66eaf252a15357","last_reissued_at":"2026-05-18T01:39:54.104260Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:54.104260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Central limit theorem for Artin $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Henry H. Kim, Peter J. Cho","submitted_at":"2015-06-24T15:13:27Z","abstract_excerpt":"We show that the sum of the traces of Frobenius elements of Artin $L$-functions in a family of $G$-fields satisfies the Gaussian distribution under certain counting conjectures. We prove the counting conjectures for $S_4$ and $S_5$-fields. We also show central limit theorem for modular form $L$-functions with the trivial central character with respect to congruence subgroups as the level goes to infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07416","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1506.07416","created_at":"2026-05-18T01:39:54.104327+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.07416v1","created_at":"2026-05-18T01:39:54.104327+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07416","created_at":"2026-05-18T01:39:54.104327+00:00"},{"alias_kind":"pith_short_12","alias_value":"6CYSL2KZ7UJG","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6CYSL2KZ7UJGBHQ3","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6CYSL2KZ","created_at":"2026-05-18T12:29:07.941421+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6CYSL2KZ7UJGBHQ3CMNRPE2K4T","json":"https://pith.science/pith/6CYSL2KZ7UJGBHQ3CMNRPE2K4T.json","graph_json":"https://pith.science/api/pith-number/6CYSL2KZ7UJGBHQ3CMNRPE2K4T/graph.json","events_json":"https://pith.science/api/pith-number/6CYSL2KZ7UJGBHQ3CMNRPE2K4T/events.json","paper":"https://pith.science/paper/6CYSL2KZ"},"agent_actions":{"view_html":"https://pith.science/pith/6CYSL2KZ7UJGBHQ3CMNRPE2K4T","download_json":"https://pith.science/pith/6CYSL2KZ7UJGBHQ3CMNRPE2K4T.json","view_paper":"https://pith.science/paper/6CYSL2KZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.07416&json=true","fetch_graph":"https://pith.science/api/pith-number/6CYSL2KZ7UJGBHQ3CMNRPE2K4T/graph.json","fetch_events":"https://pith.science/api/pith-number/6CYSL2KZ7UJGBHQ3CMNRPE2K4T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6CYSL2KZ7UJGBHQ3CMNRPE2K4T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6CYSL2KZ7UJGBHQ3CMNRPE2K4T/action/storage_attestation","attest_author":"https://pith.science/pith/6CYSL2KZ7UJGBHQ3CMNRPE2K4T/action/author_attestation","sign_citation":"https://pith.science/pith/6CYSL2KZ7UJGBHQ3CMNRPE2K4T/action/citation_signature","submit_replication":"https://pith.science/pith/6CYSL2KZ7UJGBHQ3CMNRPE2K4T/action/replication_record"}},"created_at":"2026-05-18T01:39:54.104327+00:00","updated_at":"2026-05-18T01:39:54.104327+00:00"}