Construction of All Cubic Fields of a Fixed Fundamental Discriminant (Renate Scheidler)

Hambleton, Samuel A.; Williams, H. C.

doi:10.1007/978-3-030-01404-9_4

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2020

Publication Types

Select...

Other1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For instance, cubic function fields of fixed (resp. bounded) discriminant are constructed and counted in [2,13] (using class field theory), [22] (using an algorithmic implementation of Kummer theory, applicable to a larger class of field extensions), [14,15] (building on the algorithm of [1]), and [4,17] (building on results of Shanks for cubic number fields, see e.g. [20]).…”

Section: Introductionmentioning

confidence: 99%

Cubic function fields with prescribed ramification

Karemaker,

Marques,

Sijsling

2020

Preprint

View full text Add to dashboard Cite

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 Möbius transformations on K. The article concludes by studying covers of elliptic and hyperelliptic curves that are ramified above exactly one point.

show abstract