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

Tennenhouse, M.; Williams, H. C.

doi:10.1090/S0025-5718-1986-0815853-3

A note on class-number one in certain real quadratic and pure cubic fields
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by M. Tennenhouse and H. C. Williams PDF

Math. Comp. 46 (1986), 333-336 Request permission

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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