{"paper":{"title":"Hypergeometric functions and a family of algebraic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Gautam Kalita, Rupam Barman","submitted_at":"2012-08-02T14:15:47Z","abstract_excerpt":"Let $\\lambda \\in \\mathbb{Q}\\setminus \\{0, 1\\}$ and $l \\geq 2$, and denote by $C_{l,\\lambda}$ the nonsingular projective algebraic curve over $\\mathbb{Q}$ with affine equation given by $$y^l=x(x-1)(x-\\lambda).$$ In this paper we define $\\Omega(C_{l, \\lambda})$ analogous to the real periods of elliptic curves and find a relation with ordinary hypergeometric series. We also give a relation between the number of points on $C_{l, \\lambda}$ over a finite field and Gaussian hypergeometric series. Finally we give an alternate proof of a result of \\cite{rouse}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0492","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"}