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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


The simplest cubic fields
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by Daniel Shanks PDF
Math. Comp. 28 (1974), 1137-1152 Request permission


The cyclic cubic fields generated by ${x^3} = a{x^2} + (a + 3)x + 1$ are studied in detail. The regulators are relatively small and are known at once. The class numbers are always of the form ${A^2} + 3{B^2}$, are relatively large and easy to compute. The class groups are usually easy to determine since one has the theorem that if m is divisible only by ${\text {primes}} \equiv 2\pmod 3$, then the m-rank of the class group is even. Fields with different 3-ranks are treated separately.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Math. Comp. 28 (1974), 1137-1152
  • MSC: Primary 12A50; Secondary 12A30
  • DOI:
  • MathSciNet review: 0352049