## Experimental Mathematics

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

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

Y. Lee, R. Scheidler, and C. Yarrish

#### 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

**Subjects**

Primary: 11R58: Arithmetic theory of algebraic function fields [See also 14-XX]

Secondary: 11R16: Cubic and quartic extensions 11R27: Units and factorization 14H05: Algebraic functions; function fields [See also 11R58] 11-04: Explicit machine computation and programs (not the theory of computation or programming)

**Keywords**

Purely cubic function field reduced ideal minimum fundamental unit regulator

#### 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