A note on class-number one in pure cubic fields

Hywel C Williams, Daniel Shanks

Type: Article

Publication Date: 1979-01-01

Citations: 15

DOI: https://doi.org/10.1090/s0025-5718-1979-0537977-7

Abstract

We examine a subset of the pure cubic fields wherein individual fields appear to have a probability of having class-number one approximately equal to<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="3 slash 5"><mml:semantics><mml:mrow><mml:mn>3</mml:mn><mml:mrow class="MJX-TeXAtom-ORD"><mml:mo>/</mml:mo></mml:mrow><mml:mn>5</mml:mn></mml:mrow><mml:annotation encoding="application/x-tex">3/5</mml:annotation></mml:semantics></mml:math></inline-formula>. We also suggest more elaborate but more efficient algorithms that could be used to extend the data.

Locations

Mathematics of Computation - View - PDF

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