{"paper":{"title":"A Complete Hypergeometric Point Count Formula for Dwork Hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Heidi Goodson","submitted_at":"2016-10-31T01:24:48Z","abstract_excerpt":"We extend our previous work on hypergeometric point count formulas by proving that we can express the number of points on families of Dwork hypersurfaces $$X_{\\lambda}^d: \\hspace{.1in} x_1^d+x_2^d+\\ldots+x_d^d=d\\lambda x_1x_2\\cdots x_d$$ over finite fields of order $q\\equiv 1\\pmod d$ in terms of Greene's finite field hypergeometric functions. We prove that when $d$ is odd, the number of points can be expressed as a sum of hypergeometric functions plus $(q^{d-1}-1)/(q-1)$ and conjecture that this is also true when $d$ is even. The proof rests on a result that equates certain Gauss sum expressio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09754","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"}