Open Access
Translator Disclaimer
2003 Computation of the Fundamental Units and the Regulator of a Cyclic Cubic Function Field
Y. Lee, R. Scheidler, C. Yarrish
Experiment. Math. 12(2): 211-225 (2003).

Abstract

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 {$q \equiv 1 \pmod{3}$}. 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.

Citation

Download Citation

Y. Lee. R. Scheidler. C. Yarrish. "Computation of the Fundamental Units and the Regulator of a Cyclic Cubic Function Field." Experiment. Math. 12 (2) 211 - 225, 2003.

Information

Published: 2003
First available in Project Euclid: 31 October 2003

zbMATH: 1064.11082
MathSciNet: MR2016707

Subjects:
Primary: 11R58
Secondary: 11-04 , 11R16 , 11R27 , 14H05

Keywords: fundamental unit , minimum , Purely cubic function field , reduced ideal , regulator

Rights: Copyright © 2003 A K Peters, Ltd.

JOURNAL ARTICLE
15 PAGES


SHARE
Vol.12 • No. 2 • 2003
Back to Top