Parity of class numbers and Witt equivalence of quartic fields

We show that 27 out of the 29 Witt equivalence classes of quartic number fields can be represented by fields of class number 1. It is known that the remaining two classes contain solely fields of even class numbers. We show that these two classes can be represented by fields of class number 2.

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Bibliographic Details
Published in:Mathematics of computation 1995-10, Vol.64 (212), p.1711-1715
Main Authors: Jakubec, Stanislav, Marko, František, Szymiczek, Kazimierz
Format: Article
Language:English
Subjects:
Algebra
Dyadics
Equivalence relation
Exact sciences and technology
Mathematical tables
Mathematics
Number theory
Numbers
Research article
Sciences and techniques of general use
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Description
Summary:We show that 27 out of the 29 Witt equivalence classes of quartic number fields can be represented by fields of class number 1. It is known that the remaining two classes contain solely fields of even class numbers. We show that these two classes can be represented by fields of class number 2.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-1995-1308455-1