Quadratic equations over finite fields and class numbers of real quadratic fields

被引：1

作者：

Agoh, T ^{[1
]}

Shoji, T ^{[1
]}

机构：

[1] Sci Univ Tokyo, Dept Math, Noda, Chiba 278, Japan

来源：

MONATSHEFTE FUR MATHEMATIK | 1998年 / 125卷 / 04期

关键词：

quadratic forms over finite fields; Weyl groups; hyperplane complements; partitions; combinatorial identities; class numbers; real quadratic fields;

D O I：

10.1007/BF01305343

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let p be an odd prime and F-p the finite field with p elements. In the present paper we shall investigate the number of points of certain quadratic hypersurfaces in the vector space F-p(n) and derive explicit formulas for them. In addition, we shall show that the class number of the real quadratic field Q(root p) (where p = 1 (mod 4)) over the field Q of rational numbers can be expressed by means of these formulas.

引用

页码：279 / 292

页数：14

共 8 条

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