English

Dwork hypersurfaces of degree six and Greene's hypergeometric function

Number Theory 2021-06-22 v2

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.

Keywords

Cite

@article{arxiv.2010.13079,
  title  = {Dwork hypersurfaces of degree six and Greene's hypergeometric function},
  author = {Satoshi Kumabe},
  journal= {arXiv preprint arXiv:2010.13079},
  year   = {2021}
}

Comments

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

R2 v1 2026-06-23T19:37:40.540Z