Remote Access Mathematics of Computation
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $C(3) \times C(3)$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 12A50

Retrieve articles in all journals with MSC: 12A50

Additional Information

Article copyright: © Copyright 1974 American Mathematical Society