{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RUFGZ5X2KZRGKDRAWCGKK7IUMM","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":"6468bb322859f8db8eddefe8c32c6f8ad838d6a38119778ac39e8f462d1b5cce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-19T06:49:54Z","title_canon_sha256":"dca75e1b9faa48490be5e4e585d8ef3434ec9031bd07c508af9fd7331bb4a6d9"},"schema_version":"1.0","source":{"id":"1403.4706","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4706","created_at":"2026-05-18T02:56:04Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4706v1","created_at":"2026-05-18T02:56:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4706","created_at":"2026-05-18T02:56:04Z"},{"alias_kind":"pith_short_12","alias_value":"RUFGZ5X2KZRG","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RUFGZ5X2KZRGKDRA","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RUFGZ5X2","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:2061e4123e510baab5d53ab90d4eb9be7ac3a1bd385b60efa34e8fd8d705d5f5","target":"graph","created_at":"2026-05-18T02:56:04Z","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 $f$ be a normalized Hecke eigenform with rational integer Fourier coefficients. It is an interesting question to know how often an integer $n$ has a factor common with the $n$-th Fourier coefficient of $f$. The second author \\cite{kumar3} showed that this happens very often. In this paper, we give an asymptotic formula for the number of integers $n$ for which $(n, a(n))=1$, where $a(n)$ is the $n$-th Fourier coefficient of a normalized Hecke eigenform $f$ of weight $2$ with rational integer Fourier coefficients and has complex multiplication.","authors_text":"Sanoli Gun, V. Kumar Murty","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-19T06:49:54Z","title":"A variant of Lehmer's conjecture, II: The CM-case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4706","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":"sha256:7331f6b37895f015750168e89d0228a954d55ce31a067c5aeaf3daaf4aed80f5","target":"record","created_at":"2026-05-18T02:56:04Z","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":"6468bb322859f8db8eddefe8c32c6f8ad838d6a38119778ac39e8f462d1b5cce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-19T06:49:54Z","title_canon_sha256":"dca75e1b9faa48490be5e4e585d8ef3434ec9031bd07c508af9fd7331bb4a6d9"},"schema_version":"1.0","source":{"id":"1403.4706","kind":"arxiv","version":1}},"canonical_sha256":"8d0a6cf6fa5662650e20b08ca57d14632bed4e1c6e251e4c49d2bbed410e9afa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d0a6cf6fa5662650e20b08ca57d14632bed4e1c6e251e4c49d2bbed410e9afa","first_computed_at":"2026-05-18T02:56:04.649967Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:04.649967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LjmxQBX6Od65CWKCEMke905mBwKsenwgE9KXokSdaVh9y/YhR4VVp5ugaViN/Dmsa/qO1WOZHh+v7xw9VAkyAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:04.650359Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.4706","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7331f6b37895f015750168e89d0228a954d55ce31a067c5aeaf3daaf4aed80f5","sha256:2061e4123e510baab5d53ab90d4eb9be7ac3a1bd385b60efa34e8fd8d705d5f5"],"state_sha256":"6fb5a32244f1c30c8155049f212f504f053d41828f942bda62623c7ed00010b1"}