Nagoya Mathematical Journal
- Nagoya Math. J.
- Volume 173 (2004), 163-203.
A construction of quintic rings
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.
Nagoya Math. J., Volume 173 (2004), 163-203.
First available in Project Euclid: 27 April 2005
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Kable, Anthony C.; Yukie, Akihiko. A construction of quintic rings. Nagoya Math. J. 173 (2004), 163--203. https://projecteuclid.org/euclid.nmj/1114631987