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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



$ p$-adic computation of real quadratic class numbers

Authors: J. Buchmann, J. W. Sands and H. C. Williams
Journal: Math. Comp. 54 (1990), 855-868
MSC: Primary 11Y40; Secondary 11R29
MathSciNet review: 1010596
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Abstract: Let $ \mathcal{K}$ be any real quadratic field and let $ {h_\mathcal{K}}$ be the class number of $ \mathcal{K}$. A method utilizing the p-adic class number formula for $ \mathcal{K}$ is described for evaluating $ {h_\mathcal{K}}$. The technique was programmed for a micro VAX II computer and run on all fields $ \mathcal{K}$ with radicand $ < {10^6}$.

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Article copyright: © Copyright 1990 American Mathematical Society