The class number one problem for some non-normal CM-fields of degree 2p

JOURNAL OF NUMBER THEORY

卷:132

Article

Ahn, Jeoung-Hwan²  Boutteaux, Gerard³  Kwon, Soun-Hi⁴  Louboutin, Stephane¹ 

[1] Inst Mathe Luminy, UMR 6206, F-13288 Marseille 9, France

[2] Korea Univ, Dept Math, Seoul 136701, South Korea

[3] Univ Paris 13, IUT Bobigny, Dept GEA, F-93000 Bobigny, France

[4] Korea Univ, Dept Math Educ, Seoul 136701, South Korea

关键词: CM-field;    Class number;    Dedekind zeta function;   

DOI  :  10.1016/j.jnt.2012.02.020

来源: Elsevier

【 摘 要 】

To date, the class number one problem for non-normal CM-fields is solved only for quartic CM-fields. Here, we solve it for a family of non-normal CM-fields of degree 2p, p >= 3 and odd prime. We determine all the non-isomorphic non-normal CM-fields of degree 2p, containing a real cyclic field of degree p, and of class number one. Here, p >= 3 ranges over the odd primes. There are 24 such non-isomorphic number fields: 19 of them are of degree 6 and 5 of them are of degree 10. We also construct 19 non-isomorphic non-normal CM-fields of degree 12 and of class number one, and 10 non-isomorphic non-normal CM-fields of degree 20 and of class number one. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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