## 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

## Abstract:

To calculate*R*, the regulator of a pure cubic field $Q(\sqrt [3]{{D)}}$, a complete period of Voronoiβs 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: https://doi.org/10.1090/S0025-5718-1980-0583520-4
- MathSciNet review: 583520