Continued Fractions and the Class Number of Real Quadratic Orders

被引：1

作者：

Kawamoto, Fuminori ^{[1
]}

Kishi, Yasuhiro ^{[2
]}

机构：

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

[2] Aichi Univ Educ, Dept Math, Kariya, Aichi 4488542, Japan

来源：

TOKYO JOURNAL OF MATHEMATICS | 2024年 / 47卷 / 01期

关键词：

Real quadratic fields; Class groups; Continued fractions; SUBFIELD; FIELDS;

D O I：

10.3836/tjm/1502179399

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we give a sufficient and necessary condition for a real quadratic order to have class number 1. From this, and by using Lu's results, we obtain families of real quadratic orders with non-trivial class numbers.

引用

页码：245 / 280

页数：36

共 50 条

[31] ON CLASS-NUMBER OF REAL QUADRATIC FIELDS
CHOWLA, P
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1968, 230 : 51 - &
[32] ON REAL QUADRATIC FIELDS WITH CLASS NUMBER ONE
LU, HW
KEXUE TONGBAO, 1983, 28 (01): : 134 - 135
[33] CLASS NUMBERS OF REAL QUADRATIC NUMBER FIELDS
BROWN, E
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 20 (07): : A652 - A652
[34] ON THE CLASS-NUMBER OF REAL QUADRATIC FIELDS
陆洪文
ScienceinChina,SerA., 1979, Ser.A.1979(S1) (S1) : 118 - 130
[35] On class number formula for the real quadratic fields
Sato, H
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2004, 80 (07) : 129 - 130
[36] COMPUTATION OF THE CLASS NUMBER OF A REAL QUADRATIC FIELD
MOLLIN, RA
WILLIAMS, HC
UTILITAS MATHEMATICA, 1992, 41 : 259 - 308
[37] GENERAL CRITERIA FOR DETERMINATION OF CLASS GROUPS OF REAL QUADRATIC ORDERS
Mollin, R. A.
JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, 2008, 11 (01): : 73 - 84
[38] ON SOME SUBGROUPS OF THE IDEAL CLASS GROUP OF REAL QUADRATIC ORDERS
Kawamoto, Fuminori
Kishi, Yasuhiro
Tomita, Koshi
KYUSHU JOURNAL OF MATHEMATICS, 2024, 78 (02) : 433 - 485
[39] Cyclic subgroups of ideal class groups in real quadratic orders
Mollin, RA
GLASGOW MATHEMATICAL JOURNAL, 1999, 41 : 197 - 206
[40] On the number of real quadratic fields with class number divisible by 3
Chakraborty, K
Murty, MR
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (01) : 41 - 44

← 1 2 3 4 5 →