Exponent of Class Group of Certain Imaginary Quadratic Fields

被引：0
作者：
Kalyan Chakraborty
Azizul Hoque
机构：
[1] Homi Bhabha National Institute,Harish
来源：
Czechoslovak Mathematical Journal | 2020年 / 70卷
关键词：
quadratic field; discriminant; class group; Wada’s conjecture; 11R29; 11R11;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let n > 1 be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form ℚ(x2−2yn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{Q}\left( {\sqrt {{x^2} - 2{y^n}} } \right)$$\end{document} whose ideal class group has an element of order n. This family gives a counterexample to a conjecture by H. Wada (1970) on the structure of ideal class groups.
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页码：1167 / 1178
页数：11
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