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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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Computation of the ideal class group of certain complex quartic fields
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by Richard B. Lakein PDF
Math. Comp. 28 (1974), 839-846 Request permission


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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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Math. Comp. 28 (1974), 839-846
  • MSC: Primary 12A50
  • DOI:
  • MathSciNet review: 0374090