Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

Computation of the ideal class group of certain complex quartic fields


Author: Richard B. Lakein
Journal: Math. Comp. 28 (1974), 839-846
MSC: Primary 12A50
MathSciNet review: 0374090
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Abstract: The ideal class group of quartic fields $ K = F(\sqrt \mu )$, where $ F = {\mathbf{Q}}(i)$, is calculated by a method adapted from the method of cycles of reduced ideals for real quadratic fields. The class number is found in this way for 5000 fields $ K = F(\sqrt \pi ),\pi \equiv \pm 1 \bmod 4,\pi $ a prime of F. A tabulation of the distribution of class numbers shows a striking similarity to that for real quadratic fields with prime discriminant. Also, two fields were found with noncyclic ideal class group $ C(3) \times C(3)$.


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DOI: http://dx.doi.org/10.1090/S0025-5718-1974-0374090-1
Article copyright: © Copyright 1974 American Mathematical Society