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Published in:
2008 | OriginalPaper | Chapter
Tabulation of Cubic Function Fields with Imaginary and Unusual Hessian
Authors : Pieter Rozenhart, Renate Scheidler
Published in: Algorithmic Number Theory
Publisher: Springer Berlin Heidelberg
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We give a general method for tabulating all cubic function fields over
whose discriminant
D
has odd degree, or even degree such that the leading coefficient of − 3
D
is a non-square in
, up to a given bound on
$|D| = q^{\deg(D)}$
. The main theoretical ingredient is a generalization of a theorem of Davenport and Heilbronn to cubic function fields. We present numerical data for cubic function fields over
and over
with
$\deg(D) \leq 7$
and
$\deg(D)$
odd in both cases.