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
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