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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.


Improving the speed of calculating the regulator of certain pure cubic fields
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by H. C. Williams PDF
Math. Comp. 35 (1980), 1423-1434 Request permission


To calculate R, the regulator of a pure cubic field $Q(\sqrt [3]{{D)}}$, a complete period of Voronoi’s continued fraction algorithm over $Q(\sqrt [3]{{D)}}$ is usually generated. In this paper it is shown how, in certain pure cubic fields, R can be determined by generating only about one third of this period. These results were used on a computer to find R and then the class number for all pure cubic fields $Q(\sqrt [3]{{p)}}$, where p is a prime, $p \equiv - 1\;\pmod 3$, and $p < 2 \times {10^5}$. Graphs illustrating the distribution of such cubic fields with class number one are presented.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 35 (1980), 1423-1434
  • MSC: Primary 12A30
  • DOI:
  • MathSciNet review: 583520