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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.


On the computation of the class number of an algebraic number field
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by Johannes Buchmann and H. C. Williams PDF
Math. Comp. 53 (1989), 679-688 Request permission


It is shown how the analytic class number formula can be used to produce an algorithm which efficiently computes the class number h of an algebraic number field F. The method assumes the truth of the Generalized Riemann Hypothesis in order to estimate the residue of the Dedekind zeta function of F at $s = 1$ sufficiently well that h can be determined unambiguously. Given the regulator R of F and a known divisor ${h^ \ast }$ of h, it is shown that this technique will produce the value of h in $O(|{d_F}{|^{1 + \varepsilon }}/{({h^ \ast }R)^2})$ elementary operations, where ${d_F}$ is the discriminant of F. Thus, if $h < |{d_F}{|^{1/8}}$, then the complexity of computing h (with ${h^ \ast } = 1$) is $O(|{d_F}{|^{1/4 + \varepsilon }})$.
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 53 (1989), 679-688
  • MSC: Primary 11R29; Secondary 11Y40
  • DOI:
  • MathSciNet review: 979937