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

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

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...

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Veröffentlicht in:Journal of number theory 2012-08, Vol.132 (8), p.1793-1806
Hauptverfasser: Ahn, Jeoung-Hwan, Boutteaux, Gérard, Kwon, Soun-Hi, Louboutin, Stéphane
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Sprache:eng
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Class number
CM-field
Dedekind zeta function
Mathematics
Number Theory
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container_end_page 1806
container_issue 8
container_start_page 1793
container_title Journal of number theory
container_volume 132
creator Ahn, Jeoung-Hwan
Boutteaux, Gérard
Kwon, Soun-Hi
Louboutin, Stéphane
description 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.
doi_str_mv 10.1016/j.jnt.2012.02.020
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subjects Class number
CM-field
Dedekind zeta function
Mathematics
Number Theory
title The class number one problem for some non-normal CM-fields of degree 2p
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