Hypergeometric functions over finite fields

被引：6
作者：
Otsubo, Noriyuki [1 ]
机构：
[1] Chiba Univ, Dept Math & Informat, Inage, Chiba 2638522, Japan
来源：
RAMANUJAN JOURNAL | 2024年 / 63卷 / 01期
关键词：
Hypergeometric functions; Finite fields; Exponential sums; Zeta functions; ZETA-FUNCTIONS; TRANSFORMATIONS;
D O I：
10.1007/s11139-023-00777-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a definition of generalized hypergeometric functions over finite fields using modified Gauss sums, which enables us to find clear analogy with classical hypergeometric functions over the complex numbers. We study their fundamental properties and prove summation formulas, transformation formulas and product formulas. An application to zeta functions of K3-surfaces is given. In the appendix, we give an elementary proof of the Davenport-Hasse multiplication formula for Gauss sums.
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页码：55 / 104
页数：50
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