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.
Publié le : 2003-05-14
Classification:
Purely cubic function field,
reduced ideal,
minimum,
fundamental unit,
regulator,
11R58,
11R16,
11R27,
14H05,
11-04
@article{1067634732,
author = {Lee, Y. and Scheidler, R. and Yarrish, C.},
title = {Computation of the Fundamental Units and the Regulator of a Cyclic Cubic Function Field},
journal = {Experiment. Math.},
volume = {12},
number = {1},
year = {2003},
pages = { 211-225},
language = {en},
url = {http://dml.mathdoc.fr/item/1067634732}
}
Lee, Y.; Scheidler, R.; Yarrish, C. Computation of the Fundamental Units and the Regulator of a Cyclic Cubic Function Field. Experiment. Math., Tome 12 (2003) no. 1, pp. 211-225. http://gdmltest.u-ga.fr/item/1067634732/