{"paper":{"title":"The number of $\\mathbb{F}_p$-points on Dwork hypersurfaces and hypergeometric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dermot McCarthy","submitted_at":"2016-08-19T19:02:12Z","abstract_excerpt":"We provide a formula for the number of $\\mathbb{F}_{p}$-points on the Dwork hypersurface $$x_1^n + x_2^n \\dots + x_n^n - n \\lambda \\, x_1 x_2 \\dots x_n=0$$ in terms of a $p$-adic hypergeometric function previously defined by the author. This formula holds in the general case, i.e for any $n, \\lambda \\in \\mathbb{F}_p^{*}$ and for all odd primes $p$, thus extending results of Goodson and Barman et al which hold in certain special cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05697","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"}