Determination of principal factors in $\mathcal {Q}(\sqrt {D})$ and $\mathcal {Q}(\root 3\of D)$
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- by H. C. Williams PDF
- Math. Comp. 38 (1982), 261-274 Request permission
Abstract:
Let $l = 2$ or 3 and let D be a positive l-power-free integer. Also, let R be the product of all the rational primes which completely ramify in $K = \mathcal {Q}({D^{1/l}})$. The integer d is a principal factor of the discriminant of K if $d = N(\alpha )$, where $\alpha$ is an algebraic integer of K and $d|{R^{l - 1}}$. In this paper algorithms for finding these principal factors are described. Special attention is given to the case of $l = 3$, where it is shown that Voronoi’s continued fraction algorithm can be used to find principal factors. Some results of a computer search for principal factors for all $\mathcal {Q}(\sqrt [3]{D})$ with $2 \leqslant D \leqslant 15000$ are also presented.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Math. Comp. 38 (1982), 261-274
- MSC: Primary 12A30; Secondary 12A45
- DOI: https://doi.org/10.1090/S0025-5718-1982-0637306-4
- MathSciNet review: 637306