The class number one problem for some non-abelian normal CM-fields of degree 48-Reference-Cited by-同舟云学术

The class number one problem for some non-abelian normal CM-fields of degree 48

Published:2002-10-17 Issue:242 Volume:72 Page:1003-1017
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Chang Ku-Young,Kwon Soun-Hi

Abstract

We prove that there is precisely one normal CM-field of degree 48 with class number one which has a normal CM-subfield of degree 16: the narrow Hilbert class field of Q ( 5 , 101 , θ ) \mathbb {Q}(\sqrt {5}, \sqrt {101}, \theta ) with θ 3 − θ 2 − 5 θ − 1 = 0 \theta ^3 - \theta ^2 -5 \theta -1=0 .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/2003-72-242/S0025-5718-02-01443-6/S0025-5718-02-01443-6.pdf

Reference35 articles.

1. Series in Pure Mathematics;Conner, P. E.,1988

2. Class numbers of imaginary abelian number fields;Chang, Ku-Young;Proc. Amer. Math. Soc.,2000

3. [CK2] K.-Y. Chang and S.-H. Kwon, CM-fields of degree 2𝑝𝑞, preprint.

4. [CK3] K.-Y. Chang and S.-H. Kwon, The non-abelian normal CM-fields of degree 36 with class number one, Acta Arith., 101 (2002), 53-61.

5. Some analytic bounds for zeta functions and class numbers;Hoffstein, Jeffrey;Invent. Math.,1979

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. The Class Number One Problem for Imaginary Octic Non-CM Extensions of $${\mathbb {Q}}$$;Bulletin of the Iranian Mathematical Society;2023-06-30

2. The Story of Algebraic Numbers in the First Half of the 20th Century;Springer Monographs in Mathematics;2018

3. Class number one problem for normal CM-fields;Journal of Number Theory;2007-07

4. CM-fields with relative class number one;Mathematics of Computation;2005-11-29