{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:63GMKSGBNV5LJL7ZS4XYG6HPKP","short_pith_number":"pith:63GMKSGB","schema_version":"1.0","canonical_sha256":"f6ccc548c16d7ab4aff9972f8378ef53cf4bb990f8647aceb7f2d2470550e16a","source":{"kind":"arxiv","id":"1711.00176","version":2},"attestation_state":"computed","paper":{"title":"On the Lang-Trotter conjecture for two elliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Amir Akbary, James Parks","submitted_at":"2017-11-01T02:52:37Z","abstract_excerpt":"Following Lang and Trotter we describe a probabilistic model that predicts the distribution of primes $p$ with given Frobenius traces at $p$ for two fixed elliptic curves over $\\mathbb{Q}$. In addition, we propose explicit Euler product representations for the constant in the predicted asymptotic formula and describe in detail the universal component of this constant. A new feature is that in some cases the $\\ell$-adic limits determining the $\\ell$-factors of the universal constant, unlike the Lang-Trotter conjecture for a single elliptic curve, do not stabilize. We also prove the conjecture o"},"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":"1711.00176","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-01T02:52:37Z","cross_cats_sorted":[],"title_canon_sha256":"5c51fa61257ed49f98c8527e26131bd899abd3cb2c20df89b113382986c7cc69","abstract_canon_sha256":"acc46c96a7ee8a0a7ad9fcfb40fcecadf58412154263fac9ef447141be6bd034"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:50.417932Z","signature_b64":"CAuN0vnW5GP2XQkFcjOfvMZzN6HqF33AkkC/hV9coTFjl6BjUnS/bIbfpN/L/axwgNwpgnsM97FeGFvmX0hLCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6ccc548c16d7ab4aff9972f8378ef53cf4bb990f8647aceb7f2d2470550e16a","last_reissued_at":"2026-05-18T00:30:50.417297Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:50.417297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Lang-Trotter conjecture for two elliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Amir Akbary, James Parks","submitted_at":"2017-11-01T02:52:37Z","abstract_excerpt":"Following Lang and Trotter we describe a probabilistic model that predicts the distribution of primes $p$ with given Frobenius traces at $p$ for two fixed elliptic curves over $\\mathbb{Q}$. In addition, we propose explicit Euler product representations for the constant in the predicted asymptotic formula and describe in detail the universal component of this constant. A new feature is that in some cases the $\\ell$-adic limits determining the $\\ell$-factors of the universal constant, unlike the Lang-Trotter conjecture for a single elliptic curve, do not stabilize. We also prove the conjecture o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00176","kind":"arxiv","version":2},"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":"1711.00176","created_at":"2026-05-18T00:30:50.417409+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.00176v2","created_at":"2026-05-18T00:30:50.417409+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.00176","created_at":"2026-05-18T00:30:50.417409+00:00"},{"alias_kind":"pith_short_12","alias_value":"63GMKSGBNV5L","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"63GMKSGBNV5LJL7Z","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"63GMKSGB","created_at":"2026-05-18T12:31:03.183658+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/63GMKSGBNV5LJL7ZS4XYG6HPKP","json":"https://pith.science/pith/63GMKSGBNV5LJL7ZS4XYG6HPKP.json","graph_json":"https://pith.science/api/pith-number/63GMKSGBNV5LJL7ZS4XYG6HPKP/graph.json","events_json":"https://pith.science/api/pith-number/63GMKSGBNV5LJL7ZS4XYG6HPKP/events.json","paper":"https://pith.science/paper/63GMKSGB"},"agent_actions":{"view_html":"https://pith.science/pith/63GMKSGBNV5LJL7ZS4XYG6HPKP","download_json":"https://pith.science/pith/63GMKSGBNV5LJL7ZS4XYG6HPKP.json","view_paper":"https://pith.science/paper/63GMKSGB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.00176&json=true","fetch_graph":"https://pith.science/api/pith-number/63GMKSGBNV5LJL7ZS4XYG6HPKP/graph.json","fetch_events":"https://pith.science/api/pith-number/63GMKSGBNV5LJL7ZS4XYG6HPKP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/63GMKSGBNV5LJL7ZS4XYG6HPKP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/63GMKSGBNV5LJL7ZS4XYG6HPKP/action/storage_attestation","attest_author":"https://pith.science/pith/63GMKSGBNV5LJL7ZS4XYG6HPKP/action/author_attestation","sign_citation":"https://pith.science/pith/63GMKSGBNV5LJL7ZS4XYG6HPKP/action/citation_signature","submit_replication":"https://pith.science/pith/63GMKSGBNV5LJL7ZS4XYG6HPKP/action/replication_record"}},"created_at":"2026-05-18T00:30:50.417409+00:00","updated_at":"2026-05-18T00:30:50.417409+00:00"}