On the class number of relative abelian fields.

1969 ◽  
Vol 1969 (236) ◽  
pp. 1-10 ◽  
Keyword(s):  
Class Number ◽  
Abelian Fields

A Remark on the Class Number of Abelian Fields

1954 ◽  
Vol s1-29 (4) ◽  
pp. 498-498 ◽  
Author(s):  
A. Fröhlich
Keyword(s):  
Class Number ◽  
Abelian Fields

On formulae for the class number of real Abelian fields

1996 ◽  
Vol 60 (4) ◽  
pp. 695-761 ◽  
Author(s):  
L V Kuz'min
Keyword(s):  
Class Number ◽  
Abelian Fields

Bicyclic Bicubic Fields

1990 ◽  
Vol 42 (3) ◽  
pp. 491-507 ◽  
Author(s):  
Charles J. Parry
Keyword(s):  
Class Number ◽  
Unit Group ◽  
Rational Numbers ◽  
Integral Basis ◽  
Number Problem ◽  
Biquadratic Fields ◽  
Abelian Fields ◽  
Extensive Body ◽  
Fundamental Units

There is an extensive body of literature on the bicyclic biquadratic fields. These fields provide the simplest examples of abelian noncyclic extensions of Q. In sharp contrast, there is a dearth of literature on the bicyclic bicubic extensions of the rational numbers. These fields together with the abelian noncyclic octic extensions provide the next simplest abelian noncyclic extensions.In this article, we shall study abelian bicyclic bicubic extensions of Q of degree 9. Hasse [4, v-ix] has stated as important objectives: the computation of an integral basis, the determination of class number and the calculation of fundamental units for abelian fields. In this article, we will solve the first problem completely, and show that the solution to the unit problem leads to a solution of the class number problem. Moreover, we shall give a method for determining the unit group up to a subgroup which has index 1 or 3 and so determine the class number up to a factor of 3.

scholarly journals Class number of real Abelian fields

2015 ◽  
Vol 148 ◽  
pp. 365-371 ◽  
Author(s):  
S. Jakubec ◽  
M. Pasteka ◽  
A. Schinzel
Keyword(s):  
Class Number ◽  
Abelian Fields

Note on class number parity of an abelian field of prime conductor, II

2019 ◽  
Vol 42 (1) ◽  
pp. 99-110 ◽  
Author(s):  
Humio Ichimura
Keyword(s):  
Class Number ◽  
Abelian Field
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