The number of \mathbbF_p-points on Dwork hypersurfaces and hypergeometric functions

2016/08/19 by Dermot McCarthy, McCarthy, Dermot
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Combinatorics #FOS: Mathematics #Function (biology) #Hypergeometric distribution #Hypergeometric function #Hypersurface #Mathematical physics #Mathematics #Number Theory (math.NT) #Physics #Pure mathematics #math.NT

paper · pdf · doi:10.48550/arxiv.1608.05697

openalex publication_date 2016/08/19 · arxiv created 2016/08/22 · arxiv updated 2016/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a formula for the number of \mathbbF_p-points on the Dwork hypersurface x₁ⁿ + x₂ⁿ … + x_nⁿ - n λ x₁ x₂ … 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, λ∈ \mathbbF_p^* and for all odd primes p, thus extending results of Goodson and Barman et al which hold in certain special cases.

Citations

• On the Rationality of the Zeta Function of an Algebraic Variety
• A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory

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