Tabulation of Cubic Function Fields with Imaginary and Unusual Hessian

  • Pieter Rozenhart
  • Renate Scheidler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5011)

Abstract

We give a general method for tabulating all cubic function fields over Open image in new window whose discriminant D has odd degree, or even degree such that the leading coefficient of − 3D is a non-square in Open image in new window, 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 Open image in new window and over Open image in new window with \(\deg(D) \leq 7\) and \(\deg(D)\) odd in both cases.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Pieter Rozenhart
    • 1
  • Renate Scheidler
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

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