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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

A note on class-number one in certain real quadratic and pure cubic fields


Authors: M. Tennenhouse and H. C. Williams
Journal: Math. Comp. 46 (1986), 333-336
MSC: Primary 11Y40; Secondary 11R11, 11R16
MathSciNet review: 815853
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Abstract | References | Similar Articles | Additional Information

Abstract: Let p be any odd prime and let $ h(p)$ be the class number of the real quadratic field $ \mathcal{Q}(\sqrt p )$. The results of a computer run to determine the density of the field $ \mathcal{Q}(\sqrt p )$ with $ h(p) = 1$ and $ p < {10^8}$ are presented. Similar results are given for pure cubic fields $ \mathcal{Q}(\sqrt[3]{p})$ with $ p < {10^6}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1986-0815853-3
PII: S 0025-5718(1986)0815853-3
Article copyright: © Copyright 1986 American Mathematical Society