Dwork hypersurfaces of degree six and Greene's hypergeometric function

Satoshi Kumabe

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arXiv · 2010.13079

Dwork hypersurfaces of degree six and Greene's hypergeometric function

Satoshi Kumabe

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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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BibTeX RIS

Satoshi Kumabe. 2020-10-25. Dwork hypersurfaces of degree six and Greene's hypergeometric function. https://arxiv.org/abs/2010.13079

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