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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: 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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Article copyright: © Copyright 1986 American Mathematical Society