Computations in Cubic Function Fields of Characteristic Three

2010/09/03 by Mark Bauer, Bauer, Mark, Jonathan Webster +1
Mathematics · #11Y40 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11Y40

paper · pdf · doi:10.48550/arxiv.1009.0737

arxiv created 2010/09/03 · arxiv updated 2010/09/06

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.

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