Dwork hypersurfaces of degree six and Greene's hypergeometric function

2020/10/25 by Satoshi Kumabe, Kumabe, Satoshi
Mathematics · #11T24 #14G15 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11T24 #msc:14G15

paper · pdf · doi:10.48550/arxiv.2010.13079

https://sites.google.com/view/satoshi-kumabe/home

arxiv created 2021/06/21 · arxiv updated 2021/06/22

Abstract

In this paper, we give a formula for the number of rational points on the Dwork hypersurfaces of degree six over finite fields by using Greene's finite-field hypergeometric function, which is a generalization of Goodson's formula for the Dwork hypersurfaces of degree four. Our formula is also a higher-dimensional and a finite field analogue of Matsumoto-Terasoma-Yamazaki's formula. Furthermore, we also explain the relation between our formula and Miyatani's formula.

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