{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OLVBLVVOWTFY5GINROUXF6ADYX","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":"1b0d95630f6ac6e81030af5012a973955a9cfe6b80fd86d2aa51470f665b5779","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-08-02T14:20:31Z","title_canon_sha256":"4f0aa6a22b5af8fb62c45332d21f151f1c8c466fd9e67edc7aa46986cd8a5dad"},"schema_version":"1.0","source":{"id":"1208.0495","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.0495","created_at":"2026-05-18T03:49:34Z"},{"alias_kind":"arxiv_version","alias_value":"1208.0495v1","created_at":"2026-05-18T03:49:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.0495","created_at":"2026-05-18T03:49:34Z"},{"alias_kind":"pith_short_12","alias_value":"OLVBLVVOWTFY","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OLVBLVVOWTFY5GIN","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OLVBLVVO","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:9350fb41ba55e8ee85c7379daf6b30687d68b0f84addc3c726f2757cdd75b85f","target":"graph","created_at":"2026-05-18T03:49:34Z","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 $\\lambda \\in \\mathbb{Q}\\setminus \\{0, -1\\}$ and $l \\geq 2$. Denote by $C_{l,\\lambda}$ the nonsingular projective algebraic curve over $\\mathbb{Q}$ with affine equation given by $$y^l=(x-1)(x^2+\\lambda).$$ In this paper we give a relation between the number of points on $C_{l, \\lambda}$ over a finite field and Gaussian hypergeometric series. We also give an alternate proof of a result of McCarthy (2010). We find some special values of ${_{3}}F_2$ and ${_{2}}F_1$ Gaussian hypergeometric series. Finally we evaluate the value of ${_{3}}F_2(4)$ which extends a result of Ono (1998).","authors_text":"Gautam Kalita, Rupam Barman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-08-02T14:20:31Z","title":"Certain values of Gaussian hypergeometric series and a family of algebraic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0495","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:b1fa834c4c0e2d530500ef3306584c08fb059bb71197a1fbfe4865b333c1cd7c","target":"record","created_at":"2026-05-18T03:49:34Z","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":"1b0d95630f6ac6e81030af5012a973955a9cfe6b80fd86d2aa51470f665b5779","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-08-02T14:20:31Z","title_canon_sha256":"4f0aa6a22b5af8fb62c45332d21f151f1c8c466fd9e67edc7aa46986cd8a5dad"},"schema_version":"1.0","source":{"id":"1208.0495","kind":"arxiv","version":1}},"canonical_sha256":"72ea15d6aeb4cb8e990d8ba972f803c5d8930dab0233bcecf6b3ecd4a7741766","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72ea15d6aeb4cb8e990d8ba972f803c5d8930dab0233bcecf6b3ecd4a7741766","first_computed_at":"2026-05-18T03:49:34.030726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:34.030726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GNUidDEnl4gCCcer5gd76kZn+7X6XdMpOmfF7FgoLK+WXgPnUym1n7ql2ygb6RRhtZ1ZXycT4fXgAGaGyqHkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:34.031311Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.0495","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1fa834c4c0e2d530500ef3306584c08fb059bb71197a1fbfe4865b333c1cd7c","sha256:9350fb41ba55e8ee85c7379daf6b30687d68b0f84addc3c726f2757cdd75b85f"],"state_sha256":"c8a9b1574e68df28b4205b0b1a3915b8d55d31f8828747c181a9fb643e9194cd"}