{"paper":{"title":"Evaluation of Certain Hypergeometric Functions over Finite Fields","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fang-Ting Tu, Yifan Yang","submitted_at":"2017-11-15T23:10:06Z","abstract_excerpt":"For an odd prime $p$, let $\\phi$ denote the quadratic character of the multiplicative group ${\\mathbb F}_p^\\times$, where ${\\mathbb F}_p$ is the finite field of $p$ elements. In this paper, we will obtain evaluations of the hypergeometric functions $ {}_2F_1\\left(\\begin{matrix} \\phi\\psi & \\psi\\\\ & \\phi \\end{matrix};x\\right)$, $x\\in {\\mathbb F}_p$, $x\\neq 0, 1$, over ${\\mathbb F}_p$ in terms of Hecke character attached to CM elliptic curves for characters $\\psi$ of ${\\mathbb F}_p^\\times$ of order $3$, $4$, $6$, $8$, and $12$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05842","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"}