{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:35DEQQTEVEJ5BUV5BTBAQTWTVE","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":"001dc87d18fd3650d51e9ac736a6a38dac2d1a358fdf2df65e4d1749d9e3f76b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-19T02:23:24Z","title_canon_sha256":"a49a7bd6eae8dcf015ae29193a5db624e0c00a9f5dcf88debf90eff9d0d09ffa"},"schema_version":"1.0","source":{"id":"1812.07733","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.07733","created_at":"2026-05-17T23:54:33Z"},{"alias_kind":"arxiv_version","alias_value":"1812.07733v2","created_at":"2026-05-17T23:54:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.07733","created_at":"2026-05-17T23:54:33Z"},{"alias_kind":"pith_short_12","alias_value":"35DEQQTEVEJ5","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"35DEQQTEVEJ5BUV5","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"35DEQQTE","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:445920cd3e711ba69d5ebd3c4cb1f6f5a80fe259d3c803e6eb4798cc5006a193","target":"graph","created_at":"2026-05-17T23:54:33Z","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 $k$ be an even integer and $S_k$ be the space of cusp forms of weight $k$ on $\\SL_2(\\ZZ)$. Let $S = \\oplus_{k\\in 2\\ZZ} S_k$. For $f, g\\in S$, we let $R(f, g) = \\{ (a_f(p), a_g(p)) \\in \\mathbb{P}^1(\\CC)\\ |\\ \\text{$p$ is a prime} \\}$ be the set of ratios of the Fourier coefficients of $f$ and $g$, where $a_f(n)$ (resp. $a_g(n)$) is the $n$th Fourier coefficient of $f$ (resp. $g$). In this paper, we prove that if $f$ and $g$ are nonzero and $R(f,g)$ is finite, then $f = cg$ for some constant $c$. This result is extended to the space of weakly holomorphic modular forms on $\\SL_2(\\ZZ)$. We appl","authors_text":"Dohoon Choi, Subong Lim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-19T02:23:24Z","title":"Independence between coefficients of two modular forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07733","kind":"arxiv","version":2},"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":"sha256:4f796aca67f3d11dc2dcf7adb5443a06326215a9c94a83d1fe324a9e050b5281","target":"record","created_at":"2026-05-17T23:54:33Z","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":"001dc87d18fd3650d51e9ac736a6a38dac2d1a358fdf2df65e4d1749d9e3f76b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-19T02:23:24Z","title_canon_sha256":"a49a7bd6eae8dcf015ae29193a5db624e0c00a9f5dcf88debf90eff9d0d09ffa"},"schema_version":"1.0","source":{"id":"1812.07733","kind":"arxiv","version":2}},"canonical_sha256":"df46484264a913d0d2bd0cc2084ed3a90bacbb5df1c9df554459463e37814804","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df46484264a913d0d2bd0cc2084ed3a90bacbb5df1c9df554459463e37814804","first_computed_at":"2026-05-17T23:54:33.932407Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:33.932407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gGxMMvb51HBwYTmEW5K3U4DQDiw1mrT/0dDL20pxYU4TlsNZiBn52SkhgqUpA+5DZlkxzLqbrPXzXkDnEYaXAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:33.933171Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.07733","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f796aca67f3d11dc2dcf7adb5443a06326215a9c94a83d1fe324a9e050b5281","sha256:445920cd3e711ba69d5ebd3c4cb1f6f5a80fe259d3c803e6eb4798cc5006a193"],"state_sha256":"64235ae14ff59cf7c05303cc954608c2e88de4e697581079538ca3baa8de4337"}