A construction of quintic rings
Anthony C. Kable and Akihiko Yukie
Source: Nagoya Math. J. Volume 173
(2004), 163-203.
Abstract
We construct a discriminant-preserving map from the set of orbits in the space of quadruples of quinary alternating forms over the integers to the set of isomorphism classes of quintic rings. This map may be regarded as an analogue of the famous map from the set of equivalence classes of integral binary cubic forms to the set of isomorphism classes of cubic rings and may be expected to have similar applications. We show that the ring of integers of every quintic number field lies in the image of the map. These results have been used to establish an upper bound on the number of quintic number fields with bounded discriminant.
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Permanent link to this document: http://projecteuclid.org/euclid.nmj/1114631987
Mathematical Reviews number (MathSciNet): MR2041760
Zentralblatt MATH identifier: 02111503
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