Computation of the Fundamental Units and the Regulator of a Cyclic Cubic Function Field

This paper presents algorithms for computing the two fundamental units and the regulator of a cyclic cubic extension of a rational function field over a field of order q ≡ 1 (mod 3). The procedure is based on a method originally due to Voronoi that was recently adapted to purely cubic function field...

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Bibliographic Details
Published in:Experimental mathematics 2003-01, Vol.12 (2), p.211-225, Article 211
Main Authors: Lee, Y., Scheidler, R., Yarrish, C.
Format: Article
Language:English
Subjects:
11-04
11R16
11R27
11R58
14H05
fundamental unit
minimum
Purely cubic function field
reduced ideal
regulator
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Summary:This paper presents algorithms for computing the two fundamental units and the regulator of a cyclic cubic extension of a rational function field over a field of order q ≡ 1 (mod 3). The procedure is based on a method originally due to Voronoi that was recently adapted to purely cubic function fields of unit rank one. Our numerical examples show that the two fundamental units tend to have large degree, and frequently, the extension has a very small ideal class number.
ISSN:1058-6458
1944-950X
DOI:10.1080/10586458.2003.10504493