Computations in Cubic Function Fields of Characteristic Three
Number Theory
2010-09-06 v1
Abstract
This paper contains an account of arbitrary cubic function fields of characteristic three. We define a standard form for an arbitrary cubic curve and consider its function field. By considering an integral basis for the maximal order of these function fields, we are able to calculate the field discriminant and the genus. We also describe the splitting behavior of any place, and give composition and reduction algorithms for arithmetic in the ideal class group.
Cite
@article{arxiv.1009.0737,
title = {Computations in Cubic Function Fields of Characteristic Three},
author = {Mark Bauer and Jonathan Webster},
journal= {arXiv preprint arXiv:1009.0737},
year = {2010}
}