{"paper":{"title":"Hypergeometric functions and algebraic curves $y^e=x^d+ax+b$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Pramod Kumar Kewat, Ram Kumar","submitted_at":"2016-04-26T10:48:54Z","abstract_excerpt":"Let $q$ be a prime power and $\\mathbb{F}_q$ be a finite field with $q$ elements. Let $e$ and $d$ be positive integers. In this paper, for $d\\geq2$ and $q\\equiv1(\\mathrm{mod}~ed(d-1))$, we calculate the number of points on an algebraic curve $E_{e,d}:y^e=x^d+ax+b$ over a finite field $\\mathbb{F}_q$ in terms of $_dF_{d-1}$ Gaussian hypergeometric series with multiplicative characters of orders $d$ and $e(d-1)$, and in terms of $_{d-1}F_{d-2}$ Gaussian hypergeometric series with multiplicative characters of orders $ed(d-1)$ and $e(d-1)$. This helps us to express the trace of Frobenius endomorphis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07613","kind":"arxiv","version":5},"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"}