Explicit construction of integral bases of radical function fields
Journal de Théorie des Nombres de Bordeaux, Tome 22 (2010) no. 1, pp. 259-270.

Nous donnons une construction explicite d’une base entière pour le corps de fonction K=k(t,ρ), où ρ n =Dk[t], sous l’hypothèse [K:k(t)]=n et char(k)n. Le discriminant du corps K est également calculé. Nous expliquons pourquoi ces questions sont considérablement plus faciles que dans le cas des corps de nombres. Quelques formules pour les P-signatures des corps de fonction radiciels sont également présentées dans ce papier.

We give an explicit construction of an integral basis for a radical function field K=k(t,ρ), where ρ n =Dk[t], under the assumptions [K:k(t)]=n and char(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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DOI : https://doi.org/10.5802/jtnb.714
@article{JTNB_2010__22_1_259_0,
     author = {Qingquan Wu},
     title = {Explicit construction of integral bases of radical function fields},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {259--270},
     publisher = {Universit\'e Bordeaux 1},
     volume = {22},
     number = {1},
     year = {2010},
     doi = {10.5802/jtnb.714},
     zbl = {1236.11089},
     mrnumber = {2675883},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.714/}
}
Qingquan Wu. Explicit construction of integral bases of radical function fields. Journal de Théorie des Nombres de Bordeaux, Tome 22 (2010) no. 1, pp. 259-270. doi : 10.5802/jtnb.714. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.714/

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