Note on the class numbers of certain real quadratic fields

被引：0

作者：

Humio Ichimura

机构：

[1] Yokohama City University,Department of Mathematics

来源：

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg | 2003年 / 73卷

关键词：

Prime Number; Prime Ideal; Class Number; Rational Part; Principal Ideal;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We prove that the class number of the real quadratic field\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${\mathbb{Q}}\left( {\sqrt {a^{2n} + 4} } \right)$$ \end{document} is divisible byn forany integern ≥ 2 andany odd integera ≥ 3.

引用

页码：281 / 288

页数：7

共 5 条

[1]

Gross B. H.(1978)Some results on the Mordell-Weil group of the Jacobian of the Fermat curve Invent. Math. 44 201-224

[2]

Rohrlich D. E.(1985)A note on quadratic fields in which a fixed prime number splits completely Nagoya Math. J. 99 63-71

[3]

Ichimura H.(1999)A note on quadratic fields in which a fixed prime number splits completely, III Proc. Japan Acad. 75A 176-177

[4]

Ichimura H.(1973)Real quadratic fields with class number divisible by J. Number Theory 5 237-241

[5]

Weinberger P. J.(undefined)undefined undefined undefined undefined-undefined

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