Continued Fractions and Gauss' Class Number Problem for Real Quadratic Fields

被引：3

作者：

Kawamoto, Fuminori ^{[1
]}

Tomita, Koshi ^{[2
]}

机构：

[1] Gakushuin Univ, Fac Sci, Dept Math, Toshima Ku, Tokyo 1718588, Japan

[2] Meijo Univ, Dept Math, Tenpaku Ku, Nagoya, Aichi 4688502, Japan

来源：

TOKYO JOURNAL OF MATHEMATICS | 2012年 / 35卷 / 01期

基金：

日本学术振兴会;

关键词：

Continued fractions; real quadratic fields; fundamental units; class numbers;

D O I：

10.3836/tjm/1342701351

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The main purpose of this article is to present a numerical data which shows relations between real quadratic fields of class number 1 and a mysterious behavior of the period of simple continued fraction expansion of certain quadratic irrationals. For that purpose, we define a class number, a fundamental unit, a discriminant and a Yokoi invariant for a non-square positive integer, and then see that a generalization of theorems of Siegel and of Yokoi holds. These and a theorem of Friesen and Halter-Koch imply several interesting conjectures for solving Gauss' class number problem for real quadratic fields.

引用

页码：213 / 239

页数：27

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