Dwork hypersurfaces of degree six and Greene's hypergeometric function

被引：1
|
作者：
Kumabe, Satoshi [1 ]
机构：
[1] Kyushu Univ, Fac Math, Fukuoka 8190395, Japan
来源：
HIROSHIMA MATHEMATICAL JOURNAL | 2022年 / 52卷 / 03期
关键词：
  hypergeometric functions; Dwork hypersurfaces; the number of rational points;
D O I：
10.32917/h2020097
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：287 / 310
页数：24
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