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On the infrastructure of the principal ideal class of an algebraic number field of unit rank one


Authors: Johannes Buchmann and H. C. Williams
Journal: Math. Comp. 50 (1988), 569-579
MSC: Primary 11R11; Secondary 11R16, 11R27, 11Y16, 11Y40
DOI: https://doi.org/10.1090/S0025-5718-1988-0929554-6
MathSciNet review: 929554
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Abstract | References | Similar Articles | Additional Information

Abstract: Let R be the regulator and let D be the absolute value of the discriminant of an order $ \mathcal{O}$ of an algebraic number field of unit rank 1. It is shown how the infrastructure idea of Shanks can be used to decrease the number of binary operations needed to compute R from the best known $ O(R{D^\varepsilon })$ for most continued fraction methods to $ O({R^{1/2}}{D^\varepsilon })$. These ideas can also be applied to significantly decrease the number of operations needed to determine whether or not any fractional ideal of $ \mathcal{O}$ is principal.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1988-0929554-6
Article copyright: © Copyright 1988 American Mathematical Society

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