Experimental Mathematics

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

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.

Article information

Source
Experiment. Math., Volume 12, Issue 2 (2003), 211-225.

Dates
First available in Project Euclid: 31 October 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1067634732

Mathematical Reviews number (MathSciNet)
MR2016707

Zentralblatt MATH identifier
1064.11082

Citation

Lee, Y.; Scheidler, R.; Yarrish, C. Computation of the Fundamental Units and the Regulator of a Cyclic Cubic Function Field. Experiment. Math. 12 (2003), no. 2, 211--225. https://projecteuclid.org/euclid.em/1067634732