六次Dwork超曲面与Greene超几何函数

Pub Date : 2020-10-25 DOI:10.32917/h2020097

Satoshi Kumabe

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引用次数: 1

摘要

本文利用Greene的有限域超几何函数，推广了Goodson关于四次Dwork超曲面的公式[1，定理1.1]，给出了有限域上六次Dwork超曲面上有理点个数的公式。我们的公式也是MatsumotoTerasoma-Yamazaki公式的高维有限域模拟。此外，我们还解释了我们的公式与Miyatani公式的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Dwork hypersurfaces of degree six and Greene’s hypergeometric function

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 [1, Theorem 1.1]. Our formula is also a higher-dimensional and a finite field analogue of MatsumotoTerasoma-Yamazaki's formula. Furthermore, we also explain the relation between our formula and Miyatani's formula.

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