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The class number one problem for some non-normal CM-fields of degree 2p
- Issue Date
- 8월-2012
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- CM-field; Class number; Dedekind zeta function
- Citation
- JOURNAL OF NUMBER THEORY, v.132, no.8, pp.1793 - 1806
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF NUMBER THEORY
- Volume
- 132
- Number
- 8
- Start Page
- 1793
- End Page
- 1806
- ISSN
- 0022-314X
- Abstract
- 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.
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