# Cubic function fields with prescribed ramification

@article{Karemaker2020CubicFF, title={Cubic function fields with prescribed ramification}, author={Valentijn Karemaker and Sophie Marques and Jeroen Sijsling}, journal={arXiv: Number Theory}, year={2020} }

This article describes cubic function fields $L/K$ with prescribed ramification, where $K$ is a rational function field. We give general equations for such extensions, an algorithm to obtain an explicit defining equation when the purely cubic closure $K'/K$ of $L/K$ has genus zero, and a description of the twists of $L/K$ up to isomorphism over $K$. For cubic function fields of genus at most one, we also describe the twists and isomorphism classes obtained when one allows Mobius transformations… CONTINUE READING

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