六次Dwork超曲面与Greene超几何函数

IF 0.5 4区数学 Q3 MATHEMATICS Hiroshima Mathematical Journal 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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来源期刊

Hiroshima Mathematical Journal 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Hiroshima Mathematical Journal (HMJ) is a continuation of Journal of Science of the Hiroshima University, Series A, Vol. 1 - 24 (1930 - 1960), and Journal of Science of the Hiroshima University, Series A - I , Vol. 25 - 34 (1961 - 1970). Starting with Volume 4 (1974), each volume of HMJ consists of three numbers annually. This journal publishes original papers in pure and applied mathematics. HMJ is an (electronically) open access journal from Volume 36, Number 1.