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Explicit construction of integral bases of radical function fields

Qingquan Wu — 2010

Journal de Théorie des Nombres de Bordeaux

We give an explicit construction of an integral basis for a radical function field K = k ( t , ρ ) , where ρ n = D k [ t ] , under the assumptions [ K : k ( t ) ] = n and c h a r ( k ) n . The field discriminant of K is also computed. We explain why these questions are substantially easier than the corresponding ones in number fields. Some formulae for the P -signatures of a radical function field are also discussed in this paper.

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