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A construction of quintic rings

Published online by Cambridge University Press:  22 January 2016

Anthony C. Kable  and
Akihiko Yukie
Anthony C. Kable
Affiliation:
Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, USA, [email protected]
Akihiko Yukie
Affiliation:
Mathematical Institute, Tôhoku University, Sendai, 980-8578, Japan, [email protected]
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Abstract

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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.

Keywords

11R0411R2115A7214L30
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 173 , 2004 , pp. 163 - 203
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2004

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